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

Jun 30, 2015

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

#### Explanation:

In other factorize, we need to take out common factors.
We have here;
$a c + 2 a d + 2 b c + 4 b d$
Take out $a$ as a common factor from first two variables and $2 b$ from last two variables, we get;
$= a \left(c + 2 d\right) + 2 b \left(c + 2 d\right)$
Now, again take out $\left(c + 2 d\right)$ as a common factor, we get
$= \left(c + 2 d\right) \left(a + 2 b\right)$

Jun 30, 2015

$a c + 2 a d + 2 b c + 4 b d$
$\textcolor{w h i t e}{\text{XXXX}}$$= \left(a + 2 b\right) \left(c + 2 d\right)$

#### Explanation:

Given $a c + 2 a d + 2 b c + 4 b d$

Regroup as
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{red}{\left(a c + 2 a d\right)} + \textcolor{b l u e}{\left(2 b c + 4 b d\right)}$

Extract common factor from each term independently
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{red}{\left(a\right) \left(c + 2 d\right)} + \textcolor{b l u e}{\left(2 b\right) \left(c + 2 d\right)}$

Extract the factor common to both terms
$\textcolor{w h i t e}{\text{XXXX}}$$\left(\textcolor{red}{a} + \textcolor{b l u e}{2 b}\right) \left(c + 2 d\right)$