Answer
$(5z+4)^{2}$
Work Step by Step
$25z^{2}+40z+16=$
...write first and last terms as squares.
$=(5z)^{2}+40z+4^{2}$
...does middle term equal $2ab$?
$40z=2\cdot(5z)\cdot(4)$
$=(5z)^{2}+2\cdot(5z)\cdot(4)+4^{2}$
...write as the square of a binomial.
$=(5z+4)^{2}$
