Answer
$9n^2+12n+4=(3n+2)^2$
Work Step by Step
RECALL:
Perfect square trinomials can be factored using the following formulas:
(i) $a^2+2ab+b^2=(a+b)^2$
(ii) $a^2-2ab+b^2=(a-b)^2$
The given perfect square trinomial can be written as:
$(3n)^2+2(3n)(2)+2^2$
Factor this perfect square trinomial using formula (i) above where $a=3n$ and $b=2$ to obtain:
$(3n)^2+2(3n)(2)+2^2=(3n+2)^2$
Therefore,
$9n^2+12n+4=(3n+2)^2$
