# How do you factor by grouping mn - 4m - 5n + 20?

May 25, 2015

$m n - 4 m - 5 n + 20$

$= \left(m n - 4 m\right) - \left(5 n - 20\right)$

$= m \left(n - 4\right) - 5 \left(n - 4\right)$

$= \left(m - 5\right) \left(n - 4\right)$

May 25, 2015

Given $m n - 4 m - 5 n + 20$
Notice that by extracting a common factor from the first 2 terms and a (different) common factor from the last 2 terms, we are left with $\left(n - 4\right)$ in both cases;
so
$\textcolor{red}{m n - 4 m} \textcolor{b l u e}{- 5 n + 20}$

$= \textcolor{red}{m \left(n - 4\right)} \textcolor{b l u e}{- 5 \left(n - 4\right)}$

$= \left(m - 5\right) \left(n - 4\right)$