# Difference of Squares

If a polynomial can be written as ${a}^{2}-{b}^{2}$ , then it can be factored as a difference of squares :

${a}^{2}-{b}^{2}=\left(a+b\right)\left(a-b\right)$

This is because, when you use FOIL to expand the right side, the $ab$ terms cancel out:

$\left(a+b\right)\left(a-b\right)={a}^{2}-ab+ab-{b}^{2}$

Example 1:

Factor, if possible.

${x}^{2}-64$

This is a difference of squares with $a=x$ and $b=8$ .

${x}^{2}-64=\left(x-8\right)\left(x+8\right)$

Example 2:

Factor, if possible.

$9{p}^{2}-49{q}^{2}$

This is a difference of squares with $a=3p$ and $b=7q$ .

$9{p}^{2}-49{q}^{2}=\left(3p-7q\right)\left(3p+7q\right)$

You should verify these equalities using FOIL .