## The Lesson

Some quadratic equations are in the form of a difference of squares: The quadratic equation above is a difference of squares because a square number (a number multiplied by itself) is subtracted by another. The two square numbers are:-
**x**= x × x (x squared).^{2} -
**9**= 3^{2}= 3 × 3 (3 squared).

## How to Factor a Quadratic Equation Using a Difference of Squares

A quadratic equation in the form of a difference of squares can be factored into two brackets:## How to Solve Quadratic Equations Using a Difference of Squares

Solving a quadratic equation using a difference of squares is easy.## Question

Solve the quadratic equation shown below using a difference of squares.## Step-by-Step:

# 1

Rewrite the quadratic equation as a difference of squares.
In our example,

**9**= 3 × 3 =**3**.^{2}
x

^{2}− 9 = x^{2}− 3^{2}# 2

Compare the difference of squares with the formula to find

**a**.
a = 3

# 3

Use the formula to factor the difference of squares:

x

^{2}− a^{2}= (x + a)(x − a)# 4

Substitute

**a**= 3 into the formula.
x

^{2}− 3^{2}= (x + 3)(x − 3)# 5

Rewrite the quadratic equation.

# 6

Equate the first bracket to 0 and solve to find

**x**.
x + 3 = 0 ⇒

**x = −3**# 7

Equate the second bracket to 0 and solve to find

**x**.
x − 3 = 0 ⇒

**x = 3**## Answer:

We have factored the quadratic equation using a difference of squares:**x**. We have solved the quadratic equation:

^{2}− 9 = (x + 3)(x − 3) = 0**x = −3, x = 3**.

## What Is a Difference of Squares

A difference of squares is square number (a number multiplied by itself) subtracted from another square number. An example of a difference of squares using numbers is: In general, we can use symbols instead of numbers: This can be factored into two brackets:
a

^{2}− b^{2}= (a + b)(a − b)