# Factor the expression: x^2-1

## Question:

Factor the expression:

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

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.

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}.

from Math 101: College Algebra

Chapter 4 / Lesson 10
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