Answer
$(2x+3)^2$
Work Step by Step
Rewrite $12x$ as $6x+6x$.
$4x^2+12x+9=4x^2+6x+6x+9$
Group the first two terms together and group the last two terms together.
$=(4x^2+6x)+(6x+9)$
Factor out the GCF in each group.
$=2x(2x+3)+3(2x+3)$
Factor out $(2x+3)$.
$=(2x+3)(2x+3)$
$=(2x+3)^2$
Hence, the completely factored form of the given expression is $(2x+3)^2$.
