Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter R - Review of Basic Concepts - Chapter R Test Prep - Review Exercises: 56

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