#### Answer

$(m+9)^{2}$

#### Work Step by Step

In order to factor $m^{2}$+18m+81, we must apply the rule that states that
$(a+b)^{2}$=$a^{2}$+2ab+$b^{2}$, and if we set $m^{2}$=$a^{2}$, 2ab=18m then we can solve for a and b
$m^{2}$=$a^{2}$, then to solve for a, we square root both sides
$\sqrt m^{2}$=$\sqrt a^{2}$
a=m
Then,
2ab=18m, and since we know that a=m, we can substitute in a for , then solve for b.
2ab=18a, then, to solve for b, we'll divide by 2a on both sides of the equation
$\frac{2ab}{2a}$=$\frac{18a}{2a}$
b=9
Then we sub in a and b into $(a+b)^{2}$ and get
$m^{2}$+18m+81=$(m+9)^{2}$