Multiplication

Another special binomial pattern is the product of a sum and a difference of terms. For example,

(x + 4)(x – 4) = x² – 4x + 4x – 16
= x² – 16

The middle terms are opposites, and they cancel out when combining like terms. This is not a coincidence. It always happens when multiplying a sum and difference of the same terms.

(a + b)(a – b) = a² – ab + ab – b²
= a² – b²

We get the square of the first term minus the square of the second term. You should remember this formula.

Sum and Difference Formula

(a + b)(a – b) = a² – b²