# How do you factor completely 2ax^2 - 24ax + 72a?

Apr 19, 2018

$2 a {\left(x - 6\right)}^{2}$

#### Explanation:

$\text{take out a "color(blue)"common factor } 2 a$

$= 2 a \left({x}^{2} - 12 x + 36\right)$

$\text{the factors of + 36 which sum to - 12 are - 6 and - 6}$

$= 2 a \left(x - 6\right) \left(x - 6\right) = 2 a {\left(x - 6\right)}^{2}$

Apr 19, 2018

$2 a {x}^{2} - 24 a x - 72 a = 2 a \left({x}^{2} - 12 x + 36\right) = 2 a {\left(x - 6\right)}^{2}$ because
${\left(a - b\right)}^{2} = {a}^{2} - 2 a b + {b}^{2}$ for $a = x$ and $b = 6$