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### Course: Algebra (all content) > Unit 10

Lesson 17: Factoring quadratics: Difference of squares# Factoring quadratics: Difference of squares

Learn how to factor quadratics that have the "difference of squares" form. For example, write x²-16 as (x+4)(x-4).

Factoring a polynomial involves writing it as a product of two or more polynomials. It reverses the process of polynomial multiplication.

In this article, we'll learn how to use the difference of squares pattern to factor certain polynomials. If you don't know the difference of squares pattern, please check out our video before proceeding.

## Intro: Difference of squares pattern

Every polynomial that is a difference of squares can be factored by applying the following formula:

Note that $a$ and $b$ in the pattern can be any algebraic expression. For example, for $a=x$ and $b=2$ , we get the following:

The polynomial ${x}^{2}-4$ is now expressed in factored form, $(x+2)(x-2)$ . We can expand the right-hand side of this equation to justify the factorization:

Now that we understand the pattern, let's use it to factor a few more polynomials.

## Example 1: Factoring ${x}^{2}-16$

Both ${x}^{2}$ and $16$ are ${x}^{2}=({x}{)}^{2}$ and $16=({4}{)}^{2}$ . In other words:

*perfect squares,*sinceSince the two squares are being subtracted, we can see that this polynomial represents a

*difference of squares*. We can use the**difference of squares pattern**to factor this expression:In our case, ${a}={x}$ and ${b}={4}$ . Therefore, our polynomial factors as follows:

We can check our work by ensuring the product of these two factors is ${x}^{2}-16$ .

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### Reflection question

## Example 2: Factoring $4{x}^{2}-9$

The leading coefficient does not have to equal to $1$ in order to use the difference of squares pattern. In fact, the difference of squares pattern can be used here!

This is because $4{x}^{2}$ and $9$ are $4{x}^{2}=({2x}{)}^{2}$ and $9=({3}{)}^{2}$ . We can use this information to factor the polynomial using the difference of squares pattern:

*perfect squares,*sinceA quick multiplication check verifies our answer.

### Check your understanding

## Challenge problems

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