# How to Factor a Difference of Squares (Mathematics Lesson)

# What Is the Difference of Squares?

The difference of squares is a special type of quadratic equation:# How to Factor a Difference of Squares

A difference of squares always factors to a simple expression:Expand the brackets using the FOIL method to show this is the case (see

**Note**).

# A Real Example of Factoring a Difference of Squares

**Question**: Factor and solve the difference of squares below:

**Factoring**

Step 1

Is the constant term, 9, a square number? Yes.

9 = 3

^{2}

Step 2

**a**and

**b**.

Compare a

^{2}- b

^{2}with x

^{2}- 9.

**a = x, b = 3**

Step 3

**(a + b)(a - b)**.

**Solution**

Equate the quadratic equation to 0 and solve for

**x**. Each bracket in the factored equation can be equated to 0 in turn and solved for

**x**

Step 4

Step 5

The solution to the quadratic equation x

^{2}- 9 = 0 is

**x = -3**or

**x = 3**.

# Another Real Example of How to Factor a Difference of Squares

The slider below shows another real example of how to factor a difference of squares.##### Interactive Test

**show**

##### Note

**WHAT'S IN A NAME?**

A difference of squares is so called because it is a difference (the result of subtraction) of two square numbers.

# WHY THIS FACTORING WORKS

Factoring is the opposite of expanding two brackets using the FOIL method.Let's go backwards. Start with the difference of squares factored into two brackets:

Expand the brackets using the FOIL method:

...which is a difference of squares!