# How do you factor completely a^2 + 2ac - ab - bc + c^2?

Aug 28, 2016

${a}^{2} + 2 a c - a b - b c + {c}^{2} = \left(a + c - b\right) \left(a + c\right)$

#### Explanation:

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

$= \left({a}^{2} + 2 a c + {c}^{2}\right) - \left(a b + b c\right)$

$= {\left(a + c\right)}^{2} - b \left(a + c\right)$

$= \left(\left(a + c\right) - b\right) \left(a + c\right)$

$= \left(a + c - b\right) \left(a + c\right)$