Algebra: The Remarkable Identity
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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?

  • Pythagorean theorem
  • Algebraic property
  • Remarkable identity (correct)
  • Binomial theorem
  • 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?

  • 2ab
  • a - b
  • a + b
  • (a + b)(a - b) (correct)
  • What is the purpose of the remarkable identity in algebraic manipulations?

    <p>To simplify complex expressions</p> Signup and view all the answers

    What type of expression can be simplified using the remarkable identity?

    <p>Difference of two squares</p> Signup and view all the answers

    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.

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