# How do you factor 2mx+4bx+3my+6by?

Oct 13, 2015

$\left(m + 2 b\right) \left(2 x + 3 y\right)$

#### Explanation:

Your starting expression looks like this

$2 m x + 4 b x + 3 m y + 6 b y$

If you look at the coefficients, you'll notice that you have more than one option for common factors. Moreover, the $m$ and $b$ terms can also be grouped together and used as common factors.

So, here's one way in which you can factor this expression. Use $m$ and $2 b$ as common factors

$m \cdot \left(2 x + 3 y\right) + 2 b \cdot \left(2 x + 3 y\right)$

$\left(2 x + 3 y\right) \cdot \left(m + 2 b\right)$

Alternatively, you can use $2 x$ and $3 y$ a common factors

$2 x \cdot \left(m + 2 b\right) + 3 y \cdot \left(m + 2 b\right)$

$\left(m + 2 b\right) \cdot \left(2 x + 3 y\right)$