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Home
- Elementary algebra
- Polynomials
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Key concepts
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Binomial Squares Pattern
- If
are real numbers,
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- To square a binomial: square the first term, square the last term, double their product.
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Product of Conjugates Pattern
- If
are real numbers,
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- The product is called a difference of squares.
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To multiply conjugates:
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square the first term square the last term write it as a difference of squares
Practice makes perfect
Square a Binomial Using the Binomial Squares Pattern
In the following exercises, square each binomial using the Binomial Squares Pattern.
Multiply Conjugates Using the Product of Conjugates Pattern
In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern.
Recognize and Use the Appropriate Special Product Pattern
In the following exercises, find each product.
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ⓐ
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Got questions? Get instant answers now!
Everyday math
Mental math You can use the product of conjugates pattern to multiply numbers without a calculator. Say you need to multiply 47 times 53. Think of 47 as
and 53 as
.
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ⓐ Multiply
by using the product of conjugates pattern,
.
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ⓑ Multiply
without using a calculator.
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ⓒ Which way is easier for you? Why?
Got questions? Get instant answers now!
Mental math You can use the binomial squares pattern to multiply numbers without a calculator. Say you need to square 65. Think of 65 as
.
-
ⓐ Multiply
by using the binomial squares pattern,
.
-
ⓑ Square 65 without using a calculator.
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ⓒ Which way is easier for you? Why?
ⓐ 4,225
ⓑ 4,225
ⓒ Answers will vary.
Got questions? Get instant answers now!
Writing exercises
Self check
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ On a scale of 1-10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?
Questions & Answers
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In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ.
The term pathogen came into use in the 1880s.[1][2
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respiration is the process in which we breath in oxygen and breath out carbon dioxide
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stimulates the follicle to release the mature ovum into the oviduct
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endocrine secrete hormone and regulate body process
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while pituitary gland is an example of endocrine system and it's found in the Brain
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Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
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Biology is the study of how living organisms live and survive in a specific environment
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Source:
OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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