# How to Factor a Difference of Squares

When you FOIL (multiply the *first, outside, inside,* and *last* terms together) a binomial and its conjugate, the product is called a *difference of squares.* The product of (*a* – *b*)(*a* + *b*) is *a*^{2} – *b*^{2}. Factoring a difference of squares also requires its own set of steps.

You can recognize a *difference of squares* because it’s always a binomial where both terms are perfect squares and a subtraction sign appears between them. It *always* appears as *a*^{2} – *b*^{2}, or (something)^{2} – (something else)^{2}. When you do have a difference of squares on your hands — after checking it for a Greatest Common Factor (GCF) in both terms — you follow a simple procedure: *a*^{2} – *b*^{2} = (*a* – *b*)(*a* + *b*).

For example, you can factor 25*y*^{4} – 9 with these steps:

Rewrite each term as (something)

.^{2}This example becomes (5

*y*^{2})^{2}– (3)^{2}, which clearly shows the difference of squares (“difference of” meaning subtraction).Factor the difference of squares (

*a*)– (^{2}*b*)to (^{2}*a – b*)(*a + b*).Each difference of squares (

*a*)^{2}– (*b*)^{2}always factors to (*a*–*b*)(*a*+*b*). This example factors to (5*y*^{2}*y*^{2}+ 3).