Answer
$(x+9)^2$
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:
$x^2 + 2(x)(9) + 9^2$
Factor this perfect square trinomial using formula (i) above where $a=x$ and $b=9$ to obtain:
$x^2 + 2(x)(9) + 9^2 = (x+9)^2$
Therefore,
$x^2+18x+81 = (x+9)^2$
