# How do you factor completely a^2 - ab - a + b?

Apr 6, 2016

 =color(green)( (a -1 ) ( a -b)

#### Explanation:

${a}^{2} - a b - a + b$

Factorising by grouping:

We can factor this expression by making groups of two terms:
$\left({a}^{2} - a b\right) + \left(- a + b\right)$

$a$ is common to both the terms in the first group, and $- 1$ is common to both the terms in the second group:

$= a \left(a - b\right) - 1 \left(a - b\right)$
$a - b$ is common to both the terms now:

 =color(green)( (a -1 ) ( a -b)