Answer
$y^3(2x-1)^2$
Work Step by Step
Factoring the $GCF=y^3$, then the given expression, $
4x^2y^3-4xy^3+y^3
$, is equivalent to
\begin{array}{l}
y^3(4x^2-4x+1)
.\end{array}
The two numbers whose product is $ac=
4(1)=4
$ and whose sum is $b=
-4
$ are $\{
-2,-2
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
y^3(4x^2-4x+1)
$, is
\begin{array}{l}\require{cancel}
y^3(4x^2-2x-2x+1)
\\\\=
y^3[(4x^2-2x)-(2x-1)]
\\\\=
y^3[2x(2x-1)-(2x-1)]
\\\\=
y^3[(2x-1)(2x-1)]
\\\\=
y^3(2x-1)^2
.\end{array}
