# How do you factor kx + px - ky - py?

Nov 14, 2015

$\left(k + p\right) \left(x - y\right)$

#### Explanation:

Group $k x + p x - k y - p y$
as
$\textcolor{w h i t e}{\text{XXX}} \left(k x + p x\right) - \left(k y + p y\right)$

Extract the common factor $x$ from the first term
and the common factor $y$ from the second term
$\textcolor{w h i t e}{\text{XXX}} \left(k + p\right) x - \left(k + p\right) y$

Extract $\left(k + p\right)$ as a common factor of both of these terms
$\textcolor{w h i t e}{\text{XXX}} \left(k + p\right) \left(x - y\right)$