Answer
$x^2(3y+2)^2$
Work Step by Step
Factoring the $GCF=x^2$, then the given expression, $
9y^2x^2+12yx^2+4x^2
$, is equivalent to
\begin{array}{l}
x^2(9y^2+12y+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, $
x^2(9y^2+12y+4)
$, is
\begin{array}{l}\require{cancel}
x^2(9y^2+6y+6y+4)
\\\\=
x^2[(9y^2+6y)+(6y+4)]
\\\\=
x^2[3y(3y+2)+2(3y+2)]
\\\\=
x^2[(3y+2)(3y+2)]
\\\\=
x^2(3y+2)^2
.\end{array}
