Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 8 - Polynomials and Factoring - 8-3 Multiplying Binomials - Got It? - Page 500: 4


$ 4\pi x^{2}+20\pi x+24\pi$

Work Step by Step

$S.A.=2\pi r^{2}+2\pi rh$ ...surface area of a cylinder. $=2\pi(x+2)^{2}+2\pi(x+2)(x+4)$ ...substitute $x+2$ for $r $and $x+4 $ for $h$. $=2\pi(x+2)(x+2)+2\pi(x+2)(x+4)$ ...write $(x+2)^{2}$ as $(x+2)(x+2)$. $=2\pi(x^{2}+2x+2x+4)+2\pi(x^{2}+4x+2x+8)$ ...multiply binomials. $=2\pi(x^{2}+4x+4)+2\pi(x^{2}+6x+8)$ ...factor out $ 2\pi$. $=2\pi(x^{2}+4x+4+x^{2}+6x+8)$ ...combine like terms. $=2\pi(2x^{2}+10x+12)$ ...write in standard form. $=4\pi x^{2}+20\pi x+24\pi$
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