Differences of Squares

A difference of squares is a special type of polynomial where one perfect square is subtracted from another. They would look something like:

a^2 - b^2

With these polynomials, they can be factored into two binomials with the square roots of both values. The only difference of the two binomials is that in one, the terms are added, while in the other, they are subtracted.

a^2 - b^2

= (a + b)(a - b)

If you were to FOIL (a + b)(a - b):

(a + b)(a - b)

= a^2 - ab + ab - b^2

= a^2 - b^2