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 25y^{4} – 9 with these steps:

Rewrite each term as (something)^{2}.
This example becomes (5y^{2})^{2} – (3)^{2}, which clearly shows the difference of squares (“difference of” meaning subtraction).

Factor the difference of squares (a)^{2} – (b)^{2} to (a – b)(a + b).
Each difference of squares (a)^{2} – (b)^{2} always factors to (a – b)(a + b). This example factors to (5y^{2} – 3)(5y^{2} + 3).