Answer
$(h+4)^{2}$
Work Step by Step
In order to factor $h^{2}$+8h+16, we must apply the rule that states that
$(a+b)^{2}$=$a^{2}$+2ab+$b^{2}$, and if we set $h^{2}$=$a^{2}$, 2ab=8h then we can solve for a and b
$h^{2}$=$a^{2}$, then to solve for a, we square root both sides
$\sqrt h^{2}$=$\sqrt a^{2}$
a=h
Then,
2ab=8h, and since we know that a=h, we can substitute in a for h, then solve for b.
2ab=8a, then, to solve for b, we'll divide by 2a on both sides of the equation
$\frac{2ab}{2a}$=$\frac{8a}{2a}$
b=4
Then we sub in a and b into $(a+b)^{2}$ and get
$h^{2}$+8h+16=$(h+4)^{2}$
