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Questions and Answers
What is the name of the mathematical concept illustrated in the expression (a + b)(a - b) = a^2 - b^2?
What is the name of the mathematical concept illustrated in the expression (a + b)(a - b) = a^2 - b^2?
- Pythagorean theorem
- Algebraic property
- Remarkable identity (correct)
- Binomial theorem
Which of the following expressions is equivalent to a^2 - b^2?
Which of the following expressions is equivalent to a^2 - b^2?
- 2ab
- a^2 - 2ab + b^2
- (a + b)(a - b) (correct)
- a^2 + b^2
What is the result of factoring the expression a^2 - b^2 using the remarkable identity?
What is the result of factoring the expression a^2 - b^2 using the remarkable identity?
- 2ab
- a - b
- a + b
- (a + b)(a - b) (correct)
What is the purpose of the remarkable identity in algebraic manipulations?
What is the purpose of the remarkable identity in algebraic manipulations?
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What type of expression can be simplified using the remarkable identity?
What type of expression can be simplified using the remarkable identity?
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Study Notes
The Remarkable Identity
- The mathematical concept illustrated in the expression (a + b)(a - b) = a^2 - b^2 is the difference of squares.
- The expression a^2 - b^2 is equivalent to (a + b)(a - b).
- Factoring the expression a^2 - b^2 using the remarkable identity results in (a + b)(a - b).
- The purpose of the remarkable identity in algebraic manipulations is to simplify expressions and equations by breaking them down into more manageable forms.
- The remarkable identity is used to simplify expressions of the form a^2 - b^2, which are known as differences of squares.
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Description
Solve problems related to the remarkable identity, a mathematical concept used to simplify algebraic expressions. Learn how to factor and simplify expressions using this identity.
