Answer
$(2y+1)^2$
Work Step by Step
RECALL:
$a^2+2ab+b^2=(a+b)^2$
The given trinomial can be written as:
$=(2y)^2+2(2y)(1) + 1^2$
This trinomial is in the same form as the perfect square trinomial above, where $a=2y$ and $b=1$.
Factor the perfect square trinomial using the formula above to obtain:
$=(2y+1)^2$