# How do you use the difference of two squares formula to factor 4(x + 2)² - 36?

May 2, 2015

The difference of two square formula says that ${a}^{2} + {b}^{2} = \left(a + b\right) \left(a - b\right)$

Let's call $P \left(x\right) = 4 {\left(x + 2\right)}^{2} - 36$
So here:

$a = 2 \left(x + 2\right)$
$b = 6$

So $P \left(x\right) = \left(2 \left(x + 2\right) + 6\right) \left(2 \left(x + 2\right) - 6\right)$, and it's a prime factorisation because the two factors are polynomials of degree 1, which are always irreducible.

So the answer is (if you write $2$ outside the brackets)

$P \left(x\right) = 4 \left(x + 2 + 3\right) \left(x + 2 - 3\right) = 4 \left(x + 5\right) \left(x - 1\right)$