# How do you factor (b+2)^2 - (b-2)^2?

Dec 6, 2015

$8 b$

#### Explanation:

${p}^{2} - {q}^{2} = \left(p + q\right) \left(p - q\right)$

If $p = \left(b + 2\right)$ and $q = \left(b - 2\right)$
Then the expression to be factored = $\left(\left(b + 2\right) + \left(b - 2\right)\right) \left(\left(b + 2\right) - \left(b - 2\right)\right)$
$= \left(2 b\right) \left(4\right)$
=$8 b$

This result can also be shown by simply expanding both square terms of the expression:

$\left({b}^{2} + 4 b + 4\right) - \left({b}^{2} - 4 b + 4\right) = 8 b$