# How do you factor the expression 12w^2 -27?

Dec 13, 2015

$3 \left(2 w + 3\right) \left(2 w - 3\right)$

#### Explanation:

Factor out a common multiple of both terms. In this case, it's $3$.

$3 \left(4 {w}^{2} - 9\right)$

Now, notice that $4 {w}^{2} - 9$ is a difference of squares.

A typical difference of squares in the form ${a}^{2} - {b}^{2}$ can be factorized into $\left(a + b\right) \left(a - b\right)$.

Thus, $4 {w}^{2} - 9 = \left(2 w + 3\right) \left(2 w - 3\right)$.

So, the complete factored form is:

$3 \left(2 w + 3\right) \left(2 w - 3\right)$