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 a2 – b2. 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 a2 – b2, 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: a2 – b2 = (a – b)(a + b).
For example, you can factor 25y4 – 9 with these steps:
Rewrite each term as (something)2.
This example becomes (5y2)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 (5y2 – 3)(5y2 + 3).
