# How do you factor completely ab^2 - 3b^2 - 4a + 12?

Jan 6, 2016

=color(green)((b^2-4)(a-3)

#### Explanation:

$a {b}^{2} - 3 {b}^{2} - 4 a + 12$

We can make groups of two to factorise this expression:
$\left(a {b}^{2} - 3 {b}^{2}\right) + \left(- 4 a + 12\right)$

${b}^{2}$ is common to both the terms in the first group, and $- 4$ is common to both the terms in the second group.
We can write the expression as :
${b}^{2} \left(a - 3\right) - 4 \left(a - 3\right)$

Now, The term $\left(a - 3\right)$ is common to both the terms
=color(green)((b^2-4)(a-3)