Answer
$(3q+2)^{2}$
Work Step by Step
$9q^{2}+12q+4=$
...write first and last terms as squares.
$=(3q)^{2}+12q+(2)^{2}$
...does middle term equal $2ab$?
$12q=2\cdot(3q)\cdot(2)$
$=(3q)^{2}+2\cdot(3q)\cdot(2)+(2)^{2}$
...write as the square of a binomial.
$=(3q+2)^{2}$
