#### Answer

$\color{blue}{8r^2+26rs-99s^2}$

#### Work Step by Step

RECALL:
$(a+b)(c+d) = ac + ad + bc + bd$ (This is popularly known as the FOIL method.)
Use the formula above with $a=2r$, $b=11s$, $c=4r$, and $d=-9s$ to obtain:
$(2r+11s)(4r-9s)
\\=2r(4r) + 2r(-9s) + (11s)(4r)+(11s)(-9s)
\\=8r^2+(-18rs)+44rs+(-99s^2)$
Combine like terms to obtain:
$\\=8r^2+(-18rs+44rs)-99s^2
\\=8r^2+(-18+44)(rs)-99s^2
\\=\color{blue}{8r^2+26rs-99s^2}$