Answer
$(t+6)^{2}$
Work Step by Step
$ 12t+36+t^{2}\qquad$..recognize perfect-square trinomial. $36$ and $t^{2}$ are squares.
$=t^{2}+2\cdot 6\cdot t+36\qquad$.. the sign of the middle term is positive. Write as $(A+B)^{2},\ A=t,\ B=6$
$=(t+6)^{2}$
