# How do you factor 8ac-2ad+4bc-bd?

Feb 17, 2017

$\left(4 c - d\right) \left(2 a + b\right)$

#### Explanation:

There are 4 terms and there is no common factor in all of them.
But it is possible to group them into two pairs to make common factors.

$\left(8 a c - 2 a d\right) + \left(4 b c - b d\right)$

$= 2 a \textcolor{b l u e}{\left(4 c - d\right)} + b \textcolor{b l u e}{\left(4 c - d\right)} \text{ }$ there is a common bracket

$= \textcolor{b l u e}{\left(4 c - d\right)} \left(2 a + b\right)$

There are now two factors.