The Lesson
Some quadratic equations are in the form of a difference of squares:
- x2 = x × x (x squared).
- 9 = 32 = 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 = 32.
x2 − 9 = x2 − 32
2
Compare the difference of squares with the formula to find a.

a = 3
3
Use the formula to factor the difference of squares:
x2 − a2 = (x + a)(x − a)
4
Substitute a = 3 into the formula.
x2 − 32 = (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: x2 − 9 = (x + 3)(x − 3) = 0. We have solved the quadratic equation: 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:

a2 − b2 = (a + b)(a − b)