# How do you factor: 3y - 6x + 4xy - 2y^2?

Aug 29, 2016

$\left(y - 2 x\right) \left(3 - 2 y\right)$

#### Explanation:

Group the terms in 'pairs'

That is $\left[3 y - 6 x\right] + \left[4 x y - 2 {y}^{2}\right]$

now factorise each 'pair' by taking out a $\textcolor{b l u e}{\text{common factor}}$

$\Rightarrow \textcolor{red}{3} \left(y - 2 x\right) \textcolor{red}{- 2 y} \left(y - 2 x\right)$

We now have a $\textcolor{b l u e}{\text{common factor}}$ of (y - 2x)

$\Rightarrow \left(y - 2 x\right) \left(\textcolor{red}{3 - 2 y}\right)$

$\Rightarrow 3 y - 6 x + 4 x y - 2 {y}^{2} = \left(y - 2 x\right) \left(3 - 2 y\right)$