# How do you factor 4x - x^2 - 4y + xy completely?

Oct 7, 2016

$\left(4 - x\right) \left(x - y\right)$

#### Explanation:

Factorise by $\textcolor{b l u e}{\text{grouping the terms}}$ as follows.

$\left[4 x - {x}^{2}\right] + \left[- 4 y + x y\right]$

now factorise each group.

$\Rightarrow \textcolor{red}{x} \textcolor{b l u e}{\left(4 - x\right)} \textcolor{red}{- y} \textcolor{b l u e}{\left(4 - x\right)}$

We now have a common factor of (4 - x).

$\Rightarrow \textcolor{b l u e}{\left(4 - x\right)} \textcolor{red}{\left(x - y\right)}$

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