Answer
$4a^2+12a+4ab+6b+b^2+9$
Work Step by Step
Using $(a+b)^2=a^2+2ab+b^2$ (or the Square of a binomial), the given expression, $
[3+(2a+b)]^2
,$ is equivalent to
\begin{array}{l}\require{cancel}
3^2+2(3)(2a+b)+(2a+b)^2
\\\\=
9+12a+6b+(2a+b)^2
\\\\=
9+12a+6b+(2a)^2+2(2a)(b)+(b)^2
\\\\=
9+12a+6b+4a^2+4ab+b^2
\\\\=
4a^2+12a+4ab+6b+b^2+9
.\end{array}
