How do you factor y= 5x^3 - 20x^2 +20x ?

Mar 24, 2018

By taking x as common and then applying middle term splitting

Explanation:

First, take $x$ and $5$ as common:
$5 {x}^{3} - 20 {x}^{2} + 20 x$
$= 5 x \left({x}^{2} - 4 x + 4\right)$

Then by middle term splitting:
$= 5 x \left({x}^{2} - 4 x + 4\right)$
$= 5 x \left({x}^{2} - 2 x - 2 x + 4\right)$
$= 5 x \left(x \left(x - 2\right) - 2 \left(x - 2\right)\right)$
$= 5 x {\left(x - 2\right)}^{2}$