# How do you factor 3x^2 y^2 -12xyz^2 +12z^4?

Oct 20, 2015

$3 {\left(x y - 2 {z}^{2}\right)}^{2}$

#### Explanation:

Temporarily replace
$\textcolor{w h i t e}{\text{XXX}} x y$ with $a$ and
$\textcolor{w h i t e}{\text{XXX}} {z}^{2}$ with $b$
so we have
$\textcolor{w h i t e}{\text{XXX}} 3 {a}^{2} - 12 a b + 12 {b}^{2}$

which factors as
color(white)("XXX")=3(a^2-4ab+4b^2

$\textcolor{w h i t e}{\text{XXX}} = 3 {\left(a - 2 b\right)}^{2}$

Restoring the values for $a$ and $b$
$\textcolor{w h i t e}{\text{XXX}} = 3 \left(x y - 2 {z}^{2}\right)$