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Factor the expression: x^2-1

Question:

Factor the expression:

{eq}x^2-1 {/eq}

Factorization of Quadratic Equation

The factorization of the quadratic equation is performed by several methods, depending on the specific equation. The factorization is done by using algebraic identities, splitting middle terms, by making the perfect square, etc.

Answer and Explanation:


Given Data

  • The given expression is: {eq}{x^2} - 1 {/eq}


Use the algebraic identity {eq}{a^2} - {b^2} = \left( {a - b} \right)\left( {a + b} \right) {/eq} to factor the given expression.

{eq}\begin{align*} {x^2} - 1 &= {x^2} - {1^2}\\ &= \left( {x + 1} \right)\left( {x - 1} \right) \end{align*} {/eq}


Thus, the factor of the algebraic expression is {eq}\left( {x + 1} \right)\left( {x - 1} \right) {/eq}.


Learn more about this topic:

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How to Use the Quadratic Formula to Solve a Quadratic Equation

from Math 101: College Algebra

Chapter 4 / Lesson 10
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