# How do you factor ab - 3a - 5b + 15?

May 23, 2015

$a b - 3 a - 5 b + 15 = \left(a - 5\right) \left(b - 3\right)$

Problem: Factor $a b - 3 a - 5 b + 15$.

Divide the terms into two groups.

$\left(a b - 3 a\right) - \left(5 b + 15\right)$ =

$\left(a b - 3 a\right) - \left(5 b - 15\right)$ =

Factor out the common terms in each group.

$a \left(b - 3\right) - 5 \left(b - 3\right)$

Factor out the common term $\left(b - 3\right)$.

Solution: $a b - 3 a - 5 b + 15 = \left(a - 5\right) \left(b - 3\right)$