#### Answer

$(2x+3)^2$

#### Work Step by Step

The two numbers whose product is $ac=
4(9)=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^2+12x+9
$, is
\begin{array}{l}\require{cancel}
4x^2+6x+6x+9
\\\\=
(4x^2+6x)+(6x+9)
\\\\=
2x(2x+3)+3(2x+3)
\\\\=
(2x+3)(2x+3)
\\\\=
(2x+3)^2
.\end{array}