Answer
$(2r+9)^{2}$
Work Step by Step
$4r^{2}+36r+81=$
...write first and last terms as squares.
$=(2r)^{2}+36r+9^{2}$
...does middle term equal $2ab$?
$36r=2\cdot(2r)\cdot(9)$
$=(2r)^{2}+2\cdot(2r)\cdot(9)+9^{2}$
...write as the square of a binomial.
$=(2r+9)^{2}$