There are five product formulas with which you should be familiar because you will use them with some regularity during your study of mathematics. The first of these is the formula for the difference of squares,(a − b)(a + b) = a2 − b2.

There are two variations on the formula for the square of a trinomial that you should know:

In each case, the first and third terms are the squares of the terms in the binomial, and the middle term is twice the product of the terms in the binomial. The sign in front of the middle term agrees with the sign between the terms in the binomial.

The fourth formula is the difference of cubes.

(a − b)(a2 + ab + b2) = a3 − b3

The fifth formula is the sum of cubes. (a + b)(a2 − ab + b2) = a3 + b3