Answer
(r+10s)(r+9s)
Work Step by Step
You are given $r^{2}$+19rs+90$s^{2}$. Factor it out:
$r^{2}$+10rs+9rs+90$s^{2}$ -break out the middle value-
($r^{2}$+10rs)+(9rs+90$s^{2}$) -group the first two and last two terms-
r(r+10s)+9s(r+10s) -Find the GCF of each grouping-
(r+9s)(r+10s) -factor out the common term-
=(r+10s)(r+9s)
