# How do you use the difference of two squares formula to factor 3(b+5)² - 48?

May 3, 2015

In this way:

$3 {\left(b + 5\right)}^{2} - 48 = 3 \left[{\left(b + 5\right)}^{2} - 16\right] =$

$= 3 \left(b + 5 - 4\right) \left(b + 5 + 4\right) = 3 \left(b + 1\right) \left(b + 9\right)$.

May 3, 2015

Difference of squares equation:
$\left({a}^{2} - {b}^{2}\right) = \left(a + b\right) \left(a - b\right)$

$3 {\left(b + 5\right)}^{-} 48$

$= 3 \left({\left(b + 5\right)}^{2} - {4}^{2}\right)$

$= 3 \left(\left(b + 5\right) + 4\right) \left(\left(b + 5\right) - 4\right)$

$= 3 \left(b + 9\right) \left(b + 1\right)$