Answer
$(z+7y)^2$
Work Step by Step
RECALL:
$a^2 + 2ab + b^2=(a+b)^2$
The given trinomial can be written as:
$=z^2 + 2(z)(7y) + (7y)^2$
Factor the trinomial using the formula above with $a=z$ and $b=7y$ to have:
$=(z+7y)^2$