# How do you factor ab + ac - 4b - 4c?

Nov 27, 2015

color(blue)((a-4)(b+c) is the factorised form of the expression.

#### Explanation:

$a b + a c - 4 b - 4 c$

We can make groups of two to factorise this expression:

color(blue)((ab +ac)) color(green)((-4b-4c)

$a$ is common to both the terms in the first group, and $- 4$ is common to both the terms in the second group.

$= \textcolor{b l u e}{a} \left(b + c\right) \textcolor{g r e e n}{- 4} \left(b + c\right)$

The term $\left(b + c\right)$ is common to both the terms:

color(blue)((a-4)(b+c) is the factorised form of the expression.