Answer
$3(a+2b)^2$
Work Step by Step
Factoring the $GCF=3$, then the given expression, $
3a^2+12ab+12b^2
$, is equivalent to $
3(a^2+4ab+4b^2)
$.\\
The two numbers whose product is $ac=
1(4)=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, $
3(a^2+4ab+4b^2)
$, is
\begin{array}{l}\require{cancel}
3(a^2+2ab+2ab+4b^2)
\\\\=
3[(a^2+2ab)+(2ab+4b^2)]
\\\\=
3[a(a+2b)+2b(a+2b)]
\\\\=
3[(a+2b)(a+2b)]
\\\\=
3(a+2b)^2
.\end{array}
