Answer
$25n^2+30n+9=(5n+3)^2$
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:
$(5n)^2+2(5n)(3)+3^2$
Factor this perfect square trinomial using formula (i) above where $a=5n$ and $b=3$ to obtain:
$(5n)^2+2(5n)(3)+3^2=(5n+3)^2$
Therefore,
$25n^2+30n+9=(5n+3)^2$
