How do you factor 3x(x - 2y)^2- (x - 2y)^3?

1 Answer
Oct 9, 2015

$2 \left(x + y\right) {\left(x - 2 y\right)}^{2}$

Explanation:

Both terms are multiple of ${\left(x - 2 y\right)}^{2}$, so we can collect it:

$3 x {\left(x - 2 y\right)}^{2} - {\left(x - 2 y\right)}^{3} = {\left(x - 2 y\right)}^{2} \left[3 x - \left(x - 2 y\right)\right]$

Simplifying the square brackets gives

$3 x - \left(x - 2 y\right) = 3 x - x + 2 y = 2 x + 2 y = 2 \left(x + y\right)$

So, the whole expression equals $2 \left(x + y\right) {\left(x - 2 y\right)}^{2}$