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## Algebra basics (ASL)

### Course: Algebra basics (ASL) > Unit 7

Lesson 7: Factoring quadratics: Difference of squares (ASL)- Factoring difference of squares: leading coefficient ≠ 1
- Factoring quadratics: Difference of squares (ASL)
- Factoring difference of squares: analyzing factorization
- Factoring difference of squares: missing values
- Factoring difference of squares: shared factors
- Difference of squares

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# Factoring quadratics: Difference of squares (ASL)

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, equals, x and b, equals, 2, we get the following:

The polynomial x, squared, minus, 4 is now expressed in factored form, left parenthesis, x, plus, 2, right parenthesis, left parenthesis, x, minus, 2, right parenthesis. 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, squared, minus, 16

Both x, squared and 16 are

*perfect squares,*since x, squared, equals, left parenthesis, start color #11accd, x, end color #11accd, right parenthesis, squared and 16, equals, left parenthesis, start color #1fab54, 4, end color #1fab54, right parenthesis, squared. In other words:Since 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, start color #11accd, a, end color #11accd, equals, start color #11accd, x, end color #11accd and start color #1fab54, b, end color #1fab54, equals, start color #1fab54, 4, end color #1fab54. Therefore, our polynomial factors as follows:

We can check our work by ensuring the product of these two factors is x, squared, minus, 16.

### Check your understanding

### Reflection question

## Example 2: Factoring 4, x, squared, minus, 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, squared and 9 are

*perfect squares,*since 4, x, squared, equals, left parenthesis, start color #11accd, 2, x, end color #11accd, right parenthesis, squared and 9, equals, left parenthesis, start color #1fab54, 3, end color #1fab54, right parenthesis, squared. We can use this information to factor the polynomial using the difference of squares pattern:A quick multiplication check verifies our answer.

### Check your understanding

## Challenge problems

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