Answer
$=x^2+22x+121$
$=(x+11)^2$
Work Step by Step
The given expression is
$=x^2+22x$
Find the value of $(\frac{b}{2})^2$.
Substitute $2$ for $b$.
$=(\frac{22}{2})^2$
Simplify.
$=(11)^2$
$=121$
Add $121$ to the given expression.
$=x^2+22x+121$
Write the the polynomial as $a^2+2ab+b^2$.
$=x^2+2(x)(11)+(11)^2$
Use perfect square trinomial pattern
$a^2+2ab+b^2=(a+b)^2$
We have $a=x$ and $b=11$.
$=(x+11)^2$
