Answer
$4x(3y-2z^2)^2$
Work Step by Step
Factoring the $GCF=4x$, then the given expression, $
36xy^2-48xyz^2+16xz^4
$, is equivalent to
\begin{array}{l}
4x(9y^2-12yz^2+4z^4)
.\end{array}
The two numbers whose product is $ac=
9(4)=36
$ and whose sum is $b=
-12
$ are $\{
-6,-6
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
4x(9y^2-12yz^2+4z^4)
$, is
\begin{array}{l}\require{cancel}
4x(9y^2-6yz^2-6yz^2+4z^4)
\\\\=
4x[(9y^2-6yz^2)-(6yz^2-4z^4)]
\\\\=
4x[3y(3y-2z^2)-2z^2(3y-2z^2)]
\\\\=
4x[(3y-2z^2)(3y-2z^2)]
\\\\=
4x(3y-2z^2)^2
.\end{array}
