# How do you factor by grouping xy + x - y - 1?

May 17, 2015

$x y + x - y - 1$

We factor this expression by making groups of 2 terms
$= \left(x y + x\right) + \left(- y - 1\right)$

Now we take the common factors out from each group
$= x \left(y + 1\right) - 1 \left(y + 1\right)$

$\left(y + 1\right)$ is a common factor to each of the terms now:
$= \left(y + 1\right) \left(x - 1\right)$

$\textcolor{g r e e n}{\left(y + 1\right) \left(x - 1\right)}$ is the Factorised form of $x y + x - y - 1$