Precalculus (6th Edition)

$\color{blue}{8r^2+26rs-99s^2}$
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: $\\=8r^2+(-18rs+44rs)-99s^2 \\=8r^2+(-18+44)(rs)-99s^2 \\=\color{blue}{8r^2+26rs-99s^2}$