# How do you factor 2a^2-2ab-24b^2?

##### 1 Answer
May 26, 2015

$2 {a}^{2} - 2 a b - 24 {b}^{2} = 2 \left({a}^{2} - a b - 12 {b}^{2}\right)$

$= 2 \left(a - 4 b\right) \left(a + 3 b\right)$

To find this, first eliminate the common scalar factor $2$.

Then note that:

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

and note that:

$12 = 4 \times 3$ and $1 = 4 - 3$.