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Massage therapy is an ancient healing modality that involves the manipulation of the body’s soft tissue in order to achieve relaxation and/ or rid the body of the pain and toxins. Massage can be relaxing or therapeutic depending on patients’ needs. Nowadays there are many different forms of massage therapy around the world, from ancient techniques to modern methods integrated with a more scientific approach. The earliest applications of massage therapy can be traced back to Egypt. Around 2000 BC, ancient Egyptians worked on the hands and feet in order to achieve a therapeutic effect for the whole body. Chinese ancient literature, Huangdi Neijing, also mentions different massage techniques and how they can help in treating bodily injuries as well as many internal diseases. During the middle ages, massage techniques were brought to and became widely used in Europe. In modern times, massage therapy is widely accepted worldwide. Many different countries and regions have developed their own regulations regarding the profession. In Canada, massage therapy is regulated in four provinces including BC, ON, NL and NB. In 2012, the four provinces have established inter-jurisdiction standards. In provinces that have not formed a regulation, massage therapists who have obtained an RMT Certificate are still under the management of the national association. How can one benefit from massage therapy? In modern society, most jobs require us to perform numerous repetitive movements or remain in the same position for long periods of time, such as: - sitting: software developers, office clerks, accountants; drivers; - standing: sales representatives; chefs, waitresses; - carrying, lifting: warehouse workers; Persons involved in sports may also suffer from sports injuries at some time during their life. All these occurrences can take their toll on the body and result in overworked, tight muscles and sore joints in the long run. Excessive work and stress can lead to a build-up of tension, anxiety, headaches, insomnia, circulation problems, etc. Massage therapy generally provides relaxation by reducing muscular tension and associated discomfort. It also relieves tension-related headaches and eye strain and promotes deeper and easier breathing. The specifically designed atmosphere during a session aids in anxiety and depression relief and relaxation enhancement. With regular massage treatments, one may develop a sense of calm and well-being, better concentration and creativity, increased job performance. Massage helps to enhance soft tissue elasticity and joint flexibility, re-establish proper muscular tone, improve circulation of blood and lymph, strengthen the immune system and promote cellular metabolism. Patients may experience a more restful sleep, increased energy levels and greater joint flexibility and thus- more range of motion. Massage therapy provides a therapeutic effect for treating many types of injuries and musculoskeletal conditions, such as strained muscles, sprained ligaments. Even more, it provides post-injury rehabilitation and post-operative repair. By improving one’s circulation, we help bring more nutrients and oxygen into the tissues and organs. When our circulation is activated, the body’s self-healing process begins, leading to a better state of health. At the College Clinic, we practice varies types of massage therapy, including: Therapeutic Massage is performed to release pain and tension, maintain muscle flexibility and get rid of the scar tissue. Patients healing from an old or new injury may experience great benefits from regular therapeutic massage treatments. Swedish Massage is the most common and well-known type of massage therapy in the West. Contrary to Asian massage, which utilizes the concept of energy and meridians, it is based on Western theories of anatomy and physiology. The Swedish massage techniques are aimed at achieving relaxation, maintaining muscle flexibility, and detoxifying the body by promoting circulation. Deep Tissue Massage Deep Tissue Massage is another form of a Swedish massage. It is a soft tissue manipulation that aims at releasing pain and tension from the muscles and fascia. It can be used for administering injury recovery, whiplash, and treatment of many chronic pain conditions. Some research has shown that, compared to conventional medical remedies, deep tissue massage is more effective and less expensive in relieving chronic pain caused by inflammation.

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CC-MAIN-2023-06

https://www.huatuoclinic.ca/massage-therapy/

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en

<urn:uuid:67466ffa-4a2a-4617-9831-3f2591d057d2>_28

Swedish Massage is the most common and well-known type of massage therapy in the West.

Massage therapy is an ancient healing modality that involves the manipulation of the body’s soft tissue in order to achieve relaxation and/ or rid the body of the pain and toxins. Massage can be relaxing or therapeutic depending on patients’ needs. Nowadays there are many different forms of massage therapy around the world, from ancient techniques to modern methods integrated with a more scientific approach. The earliest applications of massage therapy can be traced back to Egypt. Around 2000 BC, ancient Egyptians worked on the hands and feet in order to achieve a therapeutic effect for the whole body. Chinese ancient literature, Huangdi Neijing, also mentions different massage techniques and how they can help in treating bodily injuries as well as many internal diseases. During the middle ages, massage techniques were brought to and became widely used in Europe. In modern times, massage therapy is widely accepted worldwide. Many different countries and regions have developed their own regulations regarding the profession. In Canada, massage therapy is regulated in four provinces including BC, ON, NL and NB. In 2012, the four provinces have established inter-jurisdiction standards. In provinces that have not formed a regulation, massage therapists who have obtained an RMT Certificate are still under the management of the national association. How can one benefit from massage therapy? In modern society, most jobs require us to perform numerous repetitive movements or remain in the same position for long periods of time, such as: - sitting: software developers, office clerks, accountants; drivers; - standing: sales representatives; chefs, waitresses; - carrying, lifting: warehouse workers; Persons involved in sports may also suffer from sports injuries at some time during their life. All these occurrences can take their toll on the body and result in overworked, tight muscles and sore joints in the long run. Excessive work and stress can lead to a build-up of tension, anxiety, headaches, insomnia, circulation problems, etc. Massage therapy generally provides relaxation by reducing muscular tension and associated discomfort. It also relieves tension-related headaches and eye strain and promotes deeper and easier breathing. The specifically designed atmosphere during a session aids in anxiety and depression relief and relaxation enhancement. With regular massage treatments, one may develop a sense of calm and well-being, better concentration and creativity, increased job performance. Massage helps to enhance soft tissue elasticity and joint flexibility, re-establish proper muscular tone, improve circulation of blood and lymph, strengthen the immune system and promote cellular metabolism. Patients may experience a more restful sleep, increased energy levels and greater joint flexibility and thus- more range of motion. Massage therapy provides a therapeutic effect for treating many types of injuries and musculoskeletal conditions, such as strained muscles, sprained ligaments. Even more, it provides post-injury rehabilitation and post-operative repair. By improving one’s circulation, we help bring more nutrients and oxygen into the tissues and organs. When our circulation is activated, the body’s self-healing process begins, leading to a better state of health. At the College Clinic, we practice varies types of massage therapy, including: Therapeutic Massage is performed to release pain and tension, maintain muscle flexibility and get rid of the scar tissue. Patients healing from an old or new injury may experience great benefits from regular therapeutic massage treatments. Swedish Massage is the most common and well-known type of massage therapy in the West. Contrary to Asian massage, which utilizes the concept of energy and meridians, it is based on Western theories of anatomy and physiology. The Swedish massage techniques are aimed at achieving relaxation, maintaining muscle flexibility, and detoxifying the body by promoting circulation. Deep Tissue Massage Deep Tissue Massage is another form of a Swedish massage. It is a soft tissue manipulation that aims at releasing pain and tension from the muscles and fascia. It can be used for administering injury recovery, whiplash, and treatment of many chronic pain conditions. Some research has shown that, compared to conventional medical remedies, deep tissue massage is more effective and less expensive in relieving chronic pain caused by inflammation.

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CC-MAIN-2023-06

https://www.huatuoclinic.ca/massage-therapy/

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<urn:uuid:67466ffa-4a2a-4617-9831-3f2591d057d2>_29

Contrary to Asian massage, which utilizes the concept of energy and meridians, it is based on Western theories of anatomy and physiology.

Massage therapy is an ancient healing modality that involves the manipulation of the body’s soft tissue in order to achieve relaxation and/ or rid the body of the pain and toxins. Massage can be relaxing or therapeutic depending on patients’ needs. Nowadays there are many different forms of massage therapy around the world, from ancient techniques to modern methods integrated with a more scientific approach. The earliest applications of massage therapy can be traced back to Egypt. Around 2000 BC, ancient Egyptians worked on the hands and feet in order to achieve a therapeutic effect for the whole body. Chinese ancient literature, Huangdi Neijing, also mentions different massage techniques and how they can help in treating bodily injuries as well as many internal diseases. During the middle ages, massage techniques were brought to and became widely used in Europe. In modern times, massage therapy is widely accepted worldwide. Many different countries and regions have developed their own regulations regarding the profession. In Canada, massage therapy is regulated in four provinces including BC, ON, NL and NB. In 2012, the four provinces have established inter-jurisdiction standards. In provinces that have not formed a regulation, massage therapists who have obtained an RMT Certificate are still under the management of the national association. How can one benefit from massage therapy? In modern society, most jobs require us to perform numerous repetitive movements or remain in the same position for long periods of time, such as: - sitting: software developers, office clerks, accountants; drivers; - standing: sales representatives; chefs, waitresses; - carrying, lifting: warehouse workers; Persons involved in sports may also suffer from sports injuries at some time during their life. All these occurrences can take their toll on the body and result in overworked, tight muscles and sore joints in the long run. Excessive work and stress can lead to a build-up of tension, anxiety, headaches, insomnia, circulation problems, etc. Massage therapy generally provides relaxation by reducing muscular tension and associated discomfort. It also relieves tension-related headaches and eye strain and promotes deeper and easier breathing. The specifically designed atmosphere during a session aids in anxiety and depression relief and relaxation enhancement. With regular massage treatments, one may develop a sense of calm and well-being, better concentration and creativity, increased job performance. Massage helps to enhance soft tissue elasticity and joint flexibility, re-establish proper muscular tone, improve circulation of blood and lymph, strengthen the immune system and promote cellular metabolism. Patients may experience a more restful sleep, increased energy levels and greater joint flexibility and thus- more range of motion. Massage therapy provides a therapeutic effect for treating many types of injuries and musculoskeletal conditions, such as strained muscles, sprained ligaments. Even more, it provides post-injury rehabilitation and post-operative repair. By improving one’s circulation, we help bring more nutrients and oxygen into the tissues and organs. When our circulation is activated, the body’s self-healing process begins, leading to a better state of health. At the College Clinic, we practice varies types of massage therapy, including: Therapeutic Massage is performed to release pain and tension, maintain muscle flexibility and get rid of the scar tissue. Patients healing from an old or new injury may experience great benefits from regular therapeutic massage treatments. Swedish Massage is the most common and well-known type of massage therapy in the West. Contrary to Asian massage, which utilizes the concept of energy and meridians, it is based on Western theories of anatomy and physiology. The Swedish massage techniques are aimed at achieving relaxation, maintaining muscle flexibility, and detoxifying the body by promoting circulation. Deep Tissue Massage Deep Tissue Massage is another form of a Swedish massage. It is a soft tissue manipulation that aims at releasing pain and tension from the muscles and fascia. It can be used for administering injury recovery, whiplash, and treatment of many chronic pain conditions. Some research has shown that, compared to conventional medical remedies, deep tissue massage is more effective and less expensive in relieving chronic pain caused by inflammation.

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CC-MAIN-2023-06

https://www.huatuoclinic.ca/massage-therapy/

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<urn:uuid:67466ffa-4a2a-4617-9831-3f2591d057d2>_30

The Swedish massage techniques are aimed at achieving relaxation, maintaining muscle flexibility, and detoxifying the body by promoting circulation.

Massage therapy is an ancient healing modality that involves the manipulation of the body’s soft tissue in order to achieve relaxation and/ or rid the body of the pain and toxins. Massage can be relaxing or therapeutic depending on patients’ needs. Nowadays there are many different forms of massage therapy around the world, from ancient techniques to modern methods integrated with a more scientific approach. The earliest applications of massage therapy can be traced back to Egypt. Around 2000 BC, ancient Egyptians worked on the hands and feet in order to achieve a therapeutic effect for the whole body. Chinese ancient literature, Huangdi Neijing, also mentions different massage techniques and how they can help in treating bodily injuries as well as many internal diseases. During the middle ages, massage techniques were brought to and became widely used in Europe. In modern times, massage therapy is widely accepted worldwide. Many different countries and regions have developed their own regulations regarding the profession. In Canada, massage therapy is regulated in four provinces including BC, ON, NL and NB. In 2012, the four provinces have established inter-jurisdiction standards. In provinces that have not formed a regulation, massage therapists who have obtained an RMT Certificate are still under the management of the national association. How can one benefit from massage therapy? In modern society, most jobs require us to perform numerous repetitive movements or remain in the same position for long periods of time, such as: - sitting: software developers, office clerks, accountants; drivers; - standing: sales representatives; chefs, waitresses; - carrying, lifting: warehouse workers; Persons involved in sports may also suffer from sports injuries at some time during their life. All these occurrences can take their toll on the body and result in overworked, tight muscles and sore joints in the long run. Excessive work and stress can lead to a build-up of tension, anxiety, headaches, insomnia, circulation problems, etc. Massage therapy generally provides relaxation by reducing muscular tension and associated discomfort. It also relieves tension-related headaches and eye strain and promotes deeper and easier breathing. The specifically designed atmosphere during a session aids in anxiety and depression relief and relaxation enhancement. With regular massage treatments, one may develop a sense of calm and well-being, better concentration and creativity, increased job performance. Massage helps to enhance soft tissue elasticity and joint flexibility, re-establish proper muscular tone, improve circulation of blood and lymph, strengthen the immune system and promote cellular metabolism. Patients may experience a more restful sleep, increased energy levels and greater joint flexibility and thus- more range of motion. Massage therapy provides a therapeutic effect for treating many types of injuries and musculoskeletal conditions, such as strained muscles, sprained ligaments. Even more, it provides post-injury rehabilitation and post-operative repair. By improving one’s circulation, we help bring more nutrients and oxygen into the tissues and organs. When our circulation is activated, the body’s self-healing process begins, leading to a better state of health. At the College Clinic, we practice varies types of massage therapy, including: Therapeutic Massage is performed to release pain and tension, maintain muscle flexibility and get rid of the scar tissue. Patients healing from an old or new injury may experience great benefits from regular therapeutic massage treatments. Swedish Massage is the most common and well-known type of massage therapy in the West. Contrary to Asian massage, which utilizes the concept of energy and meridians, it is based on Western theories of anatomy and physiology. The Swedish massage techniques are aimed at achieving relaxation, maintaining muscle flexibility, and detoxifying the body by promoting circulation. Deep Tissue Massage Deep Tissue Massage is another form of a Swedish massage. It is a soft tissue manipulation that aims at releasing pain and tension from the muscles and fascia. It can be used for administering injury recovery, whiplash, and treatment of many chronic pain conditions. Some research has shown that, compared to conventional medical remedies, deep tissue massage is more effective and less expensive in relieving chronic pain caused by inflammation.

<urn:uuid:67466ffa-4a2a-4617-9831-3f2591d057d2>

CC-MAIN-2023-06

https://www.huatuoclinic.ca/massage-therapy/

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en

<urn:uuid:67466ffa-4a2a-4617-9831-3f2591d057d2>_31

Deep Tissue Massage Deep Tissue Massage is another form of a Swedish massage.

Massage therapy is an ancient healing modality that involves the manipulation of the body’s soft tissue in order to achieve relaxation and/ or rid the body of the pain and toxins. Massage can be relaxing or therapeutic depending on patients’ needs. Nowadays there are many different forms of massage therapy around the world, from ancient techniques to modern methods integrated with a more scientific approach. The earliest applications of massage therapy can be traced back to Egypt. Around 2000 BC, ancient Egyptians worked on the hands and feet in order to achieve a therapeutic effect for the whole body. Chinese ancient literature, Huangdi Neijing, also mentions different massage techniques and how they can help in treating bodily injuries as well as many internal diseases. During the middle ages, massage techniques were brought to and became widely used in Europe. In modern times, massage therapy is widely accepted worldwide. Many different countries and regions have developed their own regulations regarding the profession. In Canada, massage therapy is regulated in four provinces including BC, ON, NL and NB. In 2012, the four provinces have established inter-jurisdiction standards. In provinces that have not formed a regulation, massage therapists who have obtained an RMT Certificate are still under the management of the national association. How can one benefit from massage therapy? In modern society, most jobs require us to perform numerous repetitive movements or remain in the same position for long periods of time, such as: - sitting: software developers, office clerks, accountants; drivers; - standing: sales representatives; chefs, waitresses; - carrying, lifting: warehouse workers; Persons involved in sports may also suffer from sports injuries at some time during their life. All these occurrences can take their toll on the body and result in overworked, tight muscles and sore joints in the long run. Excessive work and stress can lead to a build-up of tension, anxiety, headaches, insomnia, circulation problems, etc. Massage therapy generally provides relaxation by reducing muscular tension and associated discomfort. It also relieves tension-related headaches and eye strain and promotes deeper and easier breathing. The specifically designed atmosphere during a session aids in anxiety and depression relief and relaxation enhancement. With regular massage treatments, one may develop a sense of calm and well-being, better concentration and creativity, increased job performance. Massage helps to enhance soft tissue elasticity and joint flexibility, re-establish proper muscular tone, improve circulation of blood and lymph, strengthen the immune system and promote cellular metabolism. Patients may experience a more restful sleep, increased energy levels and greater joint flexibility and thus- more range of motion. Massage therapy provides a therapeutic effect for treating many types of injuries and musculoskeletal conditions, such as strained muscles, sprained ligaments. Even more, it provides post-injury rehabilitation and post-operative repair. By improving one’s circulation, we help bring more nutrients and oxygen into the tissues and organs. When our circulation is activated, the body’s self-healing process begins, leading to a better state of health. At the College Clinic, we practice varies types of massage therapy, including: Therapeutic Massage is performed to release pain and tension, maintain muscle flexibility and get rid of the scar tissue. Patients healing from an old or new injury may experience great benefits from regular therapeutic massage treatments. Swedish Massage is the most common and well-known type of massage therapy in the West. Contrary to Asian massage, which utilizes the concept of energy and meridians, it is based on Western theories of anatomy and physiology. The Swedish massage techniques are aimed at achieving relaxation, maintaining muscle flexibility, and detoxifying the body by promoting circulation. Deep Tissue Massage Deep Tissue Massage is another form of a Swedish massage. It is a soft tissue manipulation that aims at releasing pain and tension from the muscles and fascia. It can be used for administering injury recovery, whiplash, and treatment of many chronic pain conditions. Some research has shown that, compared to conventional medical remedies, deep tissue massage is more effective and less expensive in relieving chronic pain caused by inflammation.

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CC-MAIN-2023-06

https://www.huatuoclinic.ca/massage-therapy/

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en

<urn:uuid:67466ffa-4a2a-4617-9831-3f2591d057d2>_32

It is a soft tissue manipulation that aims at releasing pain and tension from the muscles and fascia.

Massage therapy is an ancient healing modality that involves the manipulation of the body’s soft tissue in order to achieve relaxation and/ or rid the body of the pain and toxins. Massage can be relaxing or therapeutic depending on patients’ needs. Nowadays there are many different forms of massage therapy around the world, from ancient techniques to modern methods integrated with a more scientific approach. The earliest applications of massage therapy can be traced back to Egypt. Around 2000 BC, ancient Egyptians worked on the hands and feet in order to achieve a therapeutic effect for the whole body. Chinese ancient literature, Huangdi Neijing, also mentions different massage techniques and how they can help in treating bodily injuries as well as many internal diseases. During the middle ages, massage techniques were brought to and became widely used in Europe. In modern times, massage therapy is widely accepted worldwide. Many different countries and regions have developed their own regulations regarding the profession. In Canada, massage therapy is regulated in four provinces including BC, ON, NL and NB. In 2012, the four provinces have established inter-jurisdiction standards. In provinces that have not formed a regulation, massage therapists who have obtained an RMT Certificate are still under the management of the national association. How can one benefit from massage therapy? In modern society, most jobs require us to perform numerous repetitive movements or remain in the same position for long periods of time, such as: - sitting: software developers, office clerks, accountants; drivers; - standing: sales representatives; chefs, waitresses; - carrying, lifting: warehouse workers; Persons involved in sports may also suffer from sports injuries at some time during their life. All these occurrences can take their toll on the body and result in overworked, tight muscles and sore joints in the long run. Excessive work and stress can lead to a build-up of tension, anxiety, headaches, insomnia, circulation problems, etc. Massage therapy generally provides relaxation by reducing muscular tension and associated discomfort. It also relieves tension-related headaches and eye strain and promotes deeper and easier breathing. The specifically designed atmosphere during a session aids in anxiety and depression relief and relaxation enhancement. With regular massage treatments, one may develop a sense of calm and well-being, better concentration and creativity, increased job performance. Massage helps to enhance soft tissue elasticity and joint flexibility, re-establish proper muscular tone, improve circulation of blood and lymph, strengthen the immune system and promote cellular metabolism. Patients may experience a more restful sleep, increased energy levels and greater joint flexibility and thus- more range of motion. Massage therapy provides a therapeutic effect for treating many types of injuries and musculoskeletal conditions, such as strained muscles, sprained ligaments. Even more, it provides post-injury rehabilitation and post-operative repair. By improving one’s circulation, we help bring more nutrients and oxygen into the tissues and organs. When our circulation is activated, the body’s self-healing process begins, leading to a better state of health. At the College Clinic, we practice varies types of massage therapy, including: Therapeutic Massage is performed to release pain and tension, maintain muscle flexibility and get rid of the scar tissue. Patients healing from an old or new injury may experience great benefits from regular therapeutic massage treatments. Swedish Massage is the most common and well-known type of massage therapy in the West. Contrary to Asian massage, which utilizes the concept of energy and meridians, it is based on Western theories of anatomy and physiology. The Swedish massage techniques are aimed at achieving relaxation, maintaining muscle flexibility, and detoxifying the body by promoting circulation. Deep Tissue Massage Deep Tissue Massage is another form of a Swedish massage. It is a soft tissue manipulation that aims at releasing pain and tension from the muscles and fascia. It can be used for administering injury recovery, whiplash, and treatment of many chronic pain conditions. Some research has shown that, compared to conventional medical remedies, deep tissue massage is more effective and less expensive in relieving chronic pain caused by inflammation.

<urn:uuid:67466ffa-4a2a-4617-9831-3f2591d057d2>

CC-MAIN-2023-06

https://www.huatuoclinic.ca/massage-therapy/

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en

<urn:uuid:67466ffa-4a2a-4617-9831-3f2591d057d2>_33

It can be used for administering injury recovery, whiplash, and treatment of many chronic pain conditions.

Massage therapy is an ancient healing modality that involves the manipulation of the body’s soft tissue in order to achieve relaxation and/ or rid the body of the pain and toxins. Massage can be relaxing or therapeutic depending on patients’ needs. Nowadays there are many different forms of massage therapy around the world, from ancient techniques to modern methods integrated with a more scientific approach. The earliest applications of massage therapy can be traced back to Egypt. Around 2000 BC, ancient Egyptians worked on the hands and feet in order to achieve a therapeutic effect for the whole body. Chinese ancient literature, Huangdi Neijing, also mentions different massage techniques and how they can help in treating bodily injuries as well as many internal diseases. During the middle ages, massage techniques were brought to and became widely used in Europe. In modern times, massage therapy is widely accepted worldwide. Many different countries and regions have developed their own regulations regarding the profession. In Canada, massage therapy is regulated in four provinces including BC, ON, NL and NB. In 2012, the four provinces have established inter-jurisdiction standards. In provinces that have not formed a regulation, massage therapists who have obtained an RMT Certificate are still under the management of the national association. How can one benefit from massage therapy? In modern society, most jobs require us to perform numerous repetitive movements or remain in the same position for long periods of time, such as: - sitting: software developers, office clerks, accountants; drivers; - standing: sales representatives; chefs, waitresses; - carrying, lifting: warehouse workers; Persons involved in sports may also suffer from sports injuries at some time during their life. All these occurrences can take their toll on the body and result in overworked, tight muscles and sore joints in the long run. Excessive work and stress can lead to a build-up of tension, anxiety, headaches, insomnia, circulation problems, etc. Massage therapy generally provides relaxation by reducing muscular tension and associated discomfort. It also relieves tension-related headaches and eye strain and promotes deeper and easier breathing. The specifically designed atmosphere during a session aids in anxiety and depression relief and relaxation enhancement. With regular massage treatments, one may develop a sense of calm and well-being, better concentration and creativity, increased job performance. Massage helps to enhance soft tissue elasticity and joint flexibility, re-establish proper muscular tone, improve circulation of blood and lymph, strengthen the immune system and promote cellular metabolism. Patients may experience a more restful sleep, increased energy levels and greater joint flexibility and thus- more range of motion. Massage therapy provides a therapeutic effect for treating many types of injuries and musculoskeletal conditions, such as strained muscles, sprained ligaments. Even more, it provides post-injury rehabilitation and post-operative repair. By improving one’s circulation, we help bring more nutrients and oxygen into the tissues and organs. When our circulation is activated, the body’s self-healing process begins, leading to a better state of health. At the College Clinic, we practice varies types of massage therapy, including: Therapeutic Massage is performed to release pain and tension, maintain muscle flexibility and get rid of the scar tissue. Patients healing from an old or new injury may experience great benefits from regular therapeutic massage treatments. Swedish Massage is the most common and well-known type of massage therapy in the West. Contrary to Asian massage, which utilizes the concept of energy and meridians, it is based on Western theories of anatomy and physiology. The Swedish massage techniques are aimed at achieving relaxation, maintaining muscle flexibility, and detoxifying the body by promoting circulation. Deep Tissue Massage Deep Tissue Massage is another form of a Swedish massage. It is a soft tissue manipulation that aims at releasing pain and tension from the muscles and fascia. It can be used for administering injury recovery, whiplash, and treatment of many chronic pain conditions. Some research has shown that, compared to conventional medical remedies, deep tissue massage is more effective and less expensive in relieving chronic pain caused by inflammation.

<urn:uuid:67466ffa-4a2a-4617-9831-3f2591d057d2>

CC-MAIN-2023-06

https://www.huatuoclinic.ca/massage-therapy/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500456.61/warc/CC-MAIN-20230207102930-20230207132930-00356.warc.gz

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<urn:uuid:67466ffa-4a2a-4617-9831-3f2591d057d2>_34

Some research has shown that, compared to conventional medical remedies, deep tissue massage is more effective and less expensive in relieving chronic pain caused by inflammation.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_0

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_1

Created by Sal Khan and Monterey Institute for Technology and Education.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500456.61/warc/CC-MAIN-20230207102930-20230207132930-00356.warc.gz

en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_3

- at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500456.61/warc/CC-MAIN-20230207102930-20230207132930-00356.warc.gz

en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_5

(At first I instinctively replied "No, he wasn't.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500456.61/warc/CC-MAIN-20230207102930-20230207132930-00356.warc.gz

en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_7

", but that is because I was too focused on your un-mathematical notation.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500456.61/warc/CC-MAIN-20230207102930-20230207132930-00356.warc.gz

en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_8

("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500456.61/warc/CC-MAIN-20230207102930-20230207132930-00356.warc.gz

en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_9

The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.)

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_10

Also, (±5²)² would equal 625, which is not the 25 we need.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_11

But he could (and should) have wrote ±5x².

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_13

(63 votes) - At1:27where did the 2 come from?

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500456.61/warc/CC-MAIN-20230207102930-20230207132930-00356.warc.gz

en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_14

(8 votes) - Sal is using the pattern created by squaring a binomial.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

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CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_15

Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_19

(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...?

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_21

in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_22

u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_25

(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_26

3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2).

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_29

(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

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CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_30

Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square?

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

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CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_31

- What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

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CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_32

(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

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CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_33

would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_34

But I guess that's going a bit too far in this context.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_35

(1 vote) - Can't the first term also be both negative and positive, i.e.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_37

(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_38

And this looks really daunting because we have something to the fourth power here.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_39

And then the middle term is to the second power.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_40

But there's something about this that might pop out at you.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

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CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_41

And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_42

And 9 is also perfect square, so maybe this is the square of some binomial.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_43

And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_44

Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right?

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

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CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_46

9 is the exact same thing as, well, it could be plus or minus 3 squared.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_49

What happens if we take 5 times plus or minus 3?

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_50

So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_51

Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right?

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_52

That's the only way we're going to get a negative over there, so let's just try it with negative 3.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_53

So what is what is 2 times 5x squared times negative 3?

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500456.61/warc/CC-MAIN-20230207102930-20230207132930-00356.warc.gz

en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_55

Well, 2 times 5x squared is 10x squared times negative 3.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

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CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_58

So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_59

5x squared minus 3 times 5x squared minus 3.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>

CC-MAIN-2023-06

https://www.khanacademy.org/math/algebra2-2018/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-special-products-2

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en

<urn:uuid:5af40327-0983-4d61-8b4d-506b4f3aecc6>_60

And we saw in the last video why this works.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

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And if you want to verify it for yourself, multiply this out.

Algebra II (2018 edition) - Difference of squares intro - Factoring using the difference of squares pattern - Factoring difference of squares: leading coefficient ≠ 1 - Difference of squares - Factoring perfect squares: negative common factor - Factoring perfect squares - Perfect squares - Factoring using the perfect square pattern - Factoring difference of squares: two variables (example 2) - Factor polynomials using structure Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Created by Sal Khan and Monterey Institute for Technology and Education. Want to join the conversation? - at "0:44" isn't Sal supposed to write (((+-5)^)^) just like he did for 9?(61 votes) - Good observation! (At first I instinctively replied "No, he wasn't. What he wrote is correct.", but that is because I was too focused on your un-mathematical notation. ("^" does not equal "²", you need to write it as "^2" if you don't have access to the "²" symbol. The symbol "^" stands for to-the-power-of, not for to-the-power-of-two.) Also, (±5²)² would equal 625, which is not the 25 we need. But he could (and should) have wrote ±5x². So you are right.(63 votes) - At1:27where did the 2 come from?(8 votes) - Sal is using the pattern created by squaring a binomial. Here's the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here's where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That's where the 2 comes from. Hope this helps.(10 votes) - Couldn't the answer also be (-5x^2+3)^2 ...? :)(7 votes) - yes, it could. in fact he can also write (-5x^2)^2 'cause if the power is even base's sign become positive. u right :)(1 vote) - I don't get how 25x^4 equals (5x^2)^2; how did Sal change the 25x^4 to (5x^2)^2 and how do you do the same with similar problems?(3 votes) - Lets say you have something like: z(x + y) In this case, you would distribute the z to x and y: z(x + y) = zx + zy Likewise, you can go backwards and factor out a z when you have: zx + zy = z(x + y) If you have: Then you distribute z to both variables: (xy)^z = (x^z) * (y^z) In this case we have: We can factor out a square (because both 25 and x^4 are perfect squares: 25x^4 = [√(25x^4)]^2 = (5x^2)^2 Notice when you distribute the exponent of 2 back to the 5 and x^2 we get: (5x^2)^2 = 25x^2^2 = 25x^4 Back where we started. Comment if you have questions.(5 votes) - what if one of the variables had an odd exponent, how would you solve then ex. 3s^7+24s(5 votes) - If you factor out 3s instead of s you'd get 3s(s^6 + 8) = 3s((s^2)^3 + 2^3) which is now 3s times the sum of cubes: 3s(s^2 + 2)(s^4 - 2s^2 +4)(1 vote) - At0:48, he says that it is (5x^2)^2 , but at0:57, he says that (3x^2) can also be (-3x^2). Can't the (5x^2)^2 also be negative?(4 votes) - Yes, Sal could have written 25𝑥⁴ = (±5𝑥²)², just like 9 = (±3)² That way we would get two choices for the middle term: −30𝑥² = 2 ∙ 5 ∙ (−3) ∙ 𝑥² −30𝑥² = 2 ∙ (−5) ∙ 3 ∙ 𝑥² Thereby, we also have two choices for the factorization: 25𝑥⁴ − 30𝑥² + 9 = (5𝑥² − 3)² 25𝑥⁴ − 30𝑥² + 9 = (−5𝑥² + 3)² which makes sense, because squaring 5𝑥² − 3 will give us the same result as squaring its opposite, namely −(5𝑥² − 3) = −5𝑥² + 3(3 votes) - How would you solve an equation with a 4th degree but doesn't factor out?(3 votes) - There is an equation called the quartic equation that can be used to solve 4th degree polynomials. Check out the wikipedia article on it for more (http://en.wikipedia.org/wiki/Quartic_function)(3 votes) - What if the last term is not a perfect square? - What you are looking at is in the form of the quadratic u^2 - 4u - 45, which factors to: (u - 9)(u + 5), so your polynomial factors to: (x^2 - 9)(x^2 + 5), which factors further to: (x - 3)(x + 3)(x^2 + 5).(3 votes) - if you can factor a 4th degree expression we can also factor an expression like 3x^8- 3y^8. would it be 3x^4 y^4 (x^4-y^4)(3 votes) - You can take it a few steps further: 3x^8 - 3y^8 = 3(x^8 - y^8) = 3(x^4 + y^4)(x^4 - y^4) = 3(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = 3(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) If you use complex numbers, you may even be able to factor the remaining 4th and 2nd degree terms. But I guess that's going a bit too far in this context.(1 vote) - Can't the first term also be both negative and positive, i.e. +-(5x^2)^2?(2 votes) We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here. And then the middle term is to the second power. But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square. And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end. Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right? So it's a perfect square. 9 is the exact same thing as, well, it could be plus or minus 3 squared. It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that. Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3. So what is what is 2 times 5x squared times negative 3? What is this? Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square. So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. 5x squared minus 3 times 5x squared minus 3. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out. You will get 25x to the fourth minus 30x squared plus 9.

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You will get 25x to the fourth minus 30x squared plus 9.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

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Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

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In Utah, there have only been a few instances of AHB attacking humans or animals.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

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Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

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CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_3

The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_4

State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_5

UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_6

If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_7

Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_8

Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_9

- Look for honey bee colonies when outdoors.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_10

Honey bees nest in a wide variety of locations.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_11

Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_12

Be especially alert when climbing, don’t put your hands where you can’t see them.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_13

- Not all honey bees are a potential threat.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_14

Foraging bees may visit campsites for water, sweets, or flowers.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_15

As long as they are away from the nest, honey bees are not defensive.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_16

Yet, a large number of bees foraging in one area may indicate a colony is nearby.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_17

Look around for the colony before camping in that area.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_18

- If you do find a colony of bees, leave them alone and keep others away.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_19

If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_21

If your pet disturbs a colony it is likely to bring the bees back to you.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_22

- Wear light-colored clothing and avoid wearing scents.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_23

- Be particularly careful when using equipment that produces vibrations or sound.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_24

- If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_25

- If attacked by honey bees, run as far and as fast as possible.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_26

Pull your shirt up over your head to protect your face.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_28

Do not enter the water because the bees may wait for you to surface for air.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_29

Remove all stingers by scraping them out once you reach shelter or outrun the bees.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_30

Seek medical attention if stung more than 15 times or if you have an allergic reaction.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_31

Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_32

Make sure the monitor knows how to spot a bee swarm or an established colony.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_33

- Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access).

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_34

Common places include sprinkler boxes, sheds, attics, vents, etc.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_35

- Areas off-campus should also be examined where students arrive and leave the school grounds.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_36

- If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_37

Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_38

- Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_39

Bees are often aggravated during landscape maintenance operations.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_41

If a colony should be disturbed, encourage students to run indoors.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_42

Call 911 when there is a stinging emergency.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_44

The nurse should be aware of proper stinger removal and the signs of allergic reactions.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_45

If possible have an anaphylactic kit, bee suit, and veil available for emergencies.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_46

- Be prepared and prevent honey bee emergencies.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_47

Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_48

Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>

CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_49

Property owners should not attempt to remove feral colonies on their own.

Since 2008 when Africanized honey bee (AHB) Apis mellifera scutellata (Lepeletier) was first detected in Southern Utah the UDAF Apiary Program has monitored its spread through the state. In Utah, there have only been a few instances of AHB attacking humans or animals. Nevertheless, if a person has no experience managing bees, it is best practice to keep clear of any encountered honey bees and to treat all colonies with the respect they deserve. The counties with known established AHB populations are Emery, Garfield, Grand, Iron, Kane, San Juan, Washington, and Wayne. State inspectors continue to track movement to new areas by testing bees from managed and feral colonies in uninfested counties. UDAF is committed to ensuring that all stakeholders are made aware whenever AHB moves into a new county. If you have additional questions or concerns regarding AHB please contact the UDAF Apiary Program at (801) 982-2313 or email@example.com. Outdoor Recreation Safety Guidelines for avoiding Africanized honey bee attacks during outdoor recreation - Always stay alert. Among a variety of venomous creatures in Utah, the Africanized honey bee is only one potential hazard. - Look for honey bee colonies when outdoors. Honey bees nest in a wide variety of locations. Be alert for groups of flying bees entering or leaving an entrance or opening and listen for buzzing sounds. Be especially alert when climbing, don’t put your hands where you can’t see them. - Not all honey bees are a potential threat. Foraging bees may visit campsites for water, sweets, or flowers. As long as they are away from the nest, honey bees are not defensive. Yet, a large number of bees foraging in one area may indicate a colony is nearby. Look around for the colony before camping in that area. - If you do find a colony of bees, leave them alone and keep others away. If it is near an area frequently used by the public, notify the local parks, Forest Service, BLM, or Department of Wildlife Resources office even if the bees seem docile. - Keep your pets under control. If your pet disturbs a colony it is likely to bring the bees back to you. - Wear light-colored clothing and avoid wearing scents. - Be particularly careful when using equipment that produces vibrations or sound. - If you know that you are allergic to bee stings, always have someone with you when doing outdoor activities and carry doctor-recommended medications with you at all times. - If attacked by honey bees, run as far and as fast as possible. Pull your shirt up over your head to protect your face. Run to shelter. Do not enter the water because the bees may wait for you to surface for air. Remove all stingers by scraping them out once you reach shelter or outrun the bees. Seek medical attention if stung more than 15 times or if you have an allergic reaction. Safety Tips for Schools Guidelines for planning for Africanized Honey Bee (AHB) safety on and around campus - Have a monitor regularly walk school grounds looking for bee swarms or colonies. Make sure the monitor knows how to spot a bee swarm or an established colony. - Keep all holes in the ground and/or buildings filled or covered (1/8’’ hole or larger allows bee access). Common places include sprinkler boxes, sheds, attics, vents, etc. - Areas off-campus should also be examined where students arrive and leave the school grounds. - If a honey bee swarm or colony is detected, the faculty should be notified to keep everyone away from the area. Arrangements to remove the swarm/colony should be made even if the bees do not appear to be threatening. - Noisy equipment such as lawnmowers or generators should be used when students are indoors or away from campus. Bees are often aggravated during landscape maintenance operations. - Teach students to leave bees alone! If a colony should be disturbed, encourage students to run indoors. Call 911 when there is a stinging emergency. - Make sure the school nurse is ready. The nurse should be aware of proper stinger removal and the signs of allergic reactions. If possible have an anaphylactic kit, bee suit, and veil available for emergencies. - Be prepared and prevent honey bee emergencies. Reassure students and faculty that most people won’t encounter AHBs and those that do are rarely seriously injured when an emergency protocol is followed. Honey Bee Removal Property owners that find a feral colony on their property should contact either a beekeeper or a pest control company for help. Property owners should not attempt to remove feral colonies on their own. A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

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CC-MAIN-2023-06

https://ag.utah.gov/farmers/plants-industry/apiary-inspection-and-beekeeping/africanized-honeybees/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:f29f02b7-26a8-4e88-ba41-9659c3f1d214>_50

A listing of beekeepers (alphabetically by city) willing to collect swarms of bees can be found here: https://beeremovalsource.com/bee-removal-list/utah/

Parrots, also known as parrots, are one of the cage animals that require good care. It should be kept as clean as possible and protected from diseases. Feeding a bird is a serious job, responsibility and effort is required. Cleaning comes first. Inside the cages, there are parts that require meticulousness such as nests and water bowls. Since this type of cage items can stay moist, bacteria and microbes can grow in it quickly. Especially if the cage material is wood, microbes can accumulate for a long time. In general, the cages are cleaned with bleach and dried. Drinkers or nests are kept in the water with bleach. The materials should not be put back into the cage before they are completely dry. If the bird cage is left without cleaning for a long time, it is also harmful to the health of the birds. Especially since parrots are sensitive animals, weekly cleaning should be done without interruption. Sometimes there may be an odor from the cage, it is because it is dirty. If more than one parrot is feeding, infectious diseases can occur. One of the most curious subjects is how to clean the cage. How to Clean Parrot Cage? Before the parrot’s cage is cleaned, the parrot should be placed in a safe place and the cleaning process should be started. The bird family consists of animals that get stressed quickly. In order not to be afraid, the cleaning order should be well established. Parrots become restless if the cage is not clean and their owner will be unhappy. Or if she wants to get out of the cage and exhibits nervous movements, the cage being dirty may be the cause. For bird keepers, part of the house is reserved for the cage. In order for the house to be hygienic, it is necessary to be as careful as possible. Those who wish can do the cleaning on a daily basis. How to Do Daily Cage Cleaning? Daily cage cleaning is simpler than weekly cleaning. First of all, it is recommended to use gloves for personal hygiene. Those who wish can use a mask during cleaning. First, the floor of the cage should be cleaned, then the paper used should be changed. Changing the paper frequently is very important. It prevents the formation of odor. Then the water bowl and the manger should be washed with detergent and plenty of water. Parrot accessories should be wiped and dried one by one. If you have difficulty in cleaning the dirt, there are cleaning products specially produced for these jobs. The ideal temperature for birds is always important. Therefore, it is necessary to pay attention to the remaining wetness. How to Do Weekly Cage Cleaning? Weekly parrot cage cleaning demands more detail. While doing the weekly cage cleaning, the following points should be considered; - The bottom of the cage should be cleaned with a cloth and a cleaner. If kept directly under water, it should be dried with a dry cloth. - The grids in the cages should be carefully wiped. - Perches are the favorite areas of birds. Sometimes the most rural areas are found here. It is suitable to be cleaned on a weekly basis. - Toys or places that contain the most bacteria. It is important for the cleanliness of the cage and the health of the bird. - If disinfectant is used, the parrot should be placed in the cage after the room has been cleaned for a few hours. - Birds are sensitive to perfumes and scents. Perfume-free cleaners should be avoided whenever possible. The bathing interval of parrots and caged birds in general should be no more than once every 15 days. Seasonal conditions are also important for the bird not to get sick. Sometimes it can take up to 1 month. If the bird is restless and is cleaning with its beak, it is time to wash it. Too much bathing should be avoided. The water should not be cold. After the parrot is bathed, it must be kept in a warm environment. Parrots’ own cleaning is as important as cage cleaning. Bird keepers should pay attention to these issues and not disrupt the cleaning in order to avoid problems. Feeding a parrot is a challenging as well as fun process. Cleaning is one of them.

<urn:uuid:0f1bca06-a9d1-405e-b0b2-2f924af34c53>

CC-MAIN-2023-06

https://papaganlar.org/en/parrot-cage-cleaning/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:0f1bca06-a9d1-405e-b0b2-2f924af34c53>_0

Parrots, also known as parrots, are one of the cage animals that require good care.

Parrots, also known as parrots, are one of the cage animals that require good care. It should be kept as clean as possible and protected from diseases. Feeding a bird is a serious job, responsibility and effort is required. Cleaning comes first. Inside the cages, there are parts that require meticulousness such as nests and water bowls. Since this type of cage items can stay moist, bacteria and microbes can grow in it quickly. Especially if the cage material is wood, microbes can accumulate for a long time. In general, the cages are cleaned with bleach and dried. Drinkers or nests are kept in the water with bleach. The materials should not be put back into the cage before they are completely dry. If the bird cage is left without cleaning for a long time, it is also harmful to the health of the birds. Especially since parrots are sensitive animals, weekly cleaning should be done without interruption. Sometimes there may be an odor from the cage, it is because it is dirty. If more than one parrot is feeding, infectious diseases can occur. One of the most curious subjects is how to clean the cage. How to Clean Parrot Cage? Before the parrot’s cage is cleaned, the parrot should be placed in a safe place and the cleaning process should be started. The bird family consists of animals that get stressed quickly. In order not to be afraid, the cleaning order should be well established. Parrots become restless if the cage is not clean and their owner will be unhappy. Or if she wants to get out of the cage and exhibits nervous movements, the cage being dirty may be the cause. For bird keepers, part of the house is reserved for the cage. In order for the house to be hygienic, it is necessary to be as careful as possible. Those who wish can do the cleaning on a daily basis. How to Do Daily Cage Cleaning? Daily cage cleaning is simpler than weekly cleaning. First of all, it is recommended to use gloves for personal hygiene. Those who wish can use a mask during cleaning. First, the floor of the cage should be cleaned, then the paper used should be changed. Changing the paper frequently is very important. It prevents the formation of odor. Then the water bowl and the manger should be washed with detergent and plenty of water. Parrot accessories should be wiped and dried one by one. If you have difficulty in cleaning the dirt, there are cleaning products specially produced for these jobs. The ideal temperature for birds is always important. Therefore, it is necessary to pay attention to the remaining wetness. How to Do Weekly Cage Cleaning? Weekly parrot cage cleaning demands more detail. While doing the weekly cage cleaning, the following points should be considered; - The bottom of the cage should be cleaned with a cloth and a cleaner. If kept directly under water, it should be dried with a dry cloth. - The grids in the cages should be carefully wiped. - Perches are the favorite areas of birds. Sometimes the most rural areas are found here. It is suitable to be cleaned on a weekly basis. - Toys or places that contain the most bacteria. It is important for the cleanliness of the cage and the health of the bird. - If disinfectant is used, the parrot should be placed in the cage after the room has been cleaned for a few hours. - Birds are sensitive to perfumes and scents. Perfume-free cleaners should be avoided whenever possible. The bathing interval of parrots and caged birds in general should be no more than once every 15 days. Seasonal conditions are also important for the bird not to get sick. Sometimes it can take up to 1 month. If the bird is restless and is cleaning with its beak, it is time to wash it. Too much bathing should be avoided. The water should not be cold. After the parrot is bathed, it must be kept in a warm environment. Parrots’ own cleaning is as important as cage cleaning. Bird keepers should pay attention to these issues and not disrupt the cleaning in order to avoid problems. Feeding a parrot is a challenging as well as fun process. Cleaning is one of them.

<urn:uuid:0f1bca06-a9d1-405e-b0b2-2f924af34c53>

CC-MAIN-2023-06

https://papaganlar.org/en/parrot-cage-cleaning/

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00436.warc.gz

en

<urn:uuid:0f1bca06-a9d1-405e-b0b2-2f924af34c53>_1

It should be kept as clean as possible and protected from diseases.