#### Answer

$(q+1)^{2}$

#### Work Step by Step

In order to factor $q^{2}$+2q+1, we must apply the rule that states that
$(a+b)^{2}$=$a^{2}$+2ab+$b^{2}$, and if we set $q^{2}$=$a^{2}$, 2ab=2q then we can solve for a and b
$q^{2}$=$a^{2}$, then to solve for a, we square root both sides
$\sqrt q^{2}$=$\sqrt a^{2}$
a=q
Then,
2ab=2q, and since we know that a=q, we can substitute in a for q, then solve for b.
2ab=2a, then, to solve for b, we'll divide by 2a on both sides of the equation
$\frac{2ab}{2a}$=$\frac{2a}{2a}$
b=1
Then we sub in a and b into $(a+b)^{2}$ and get
$q^{2}$+2q+1=$(q+1)^{2}$