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 - Practice and Problem-Solving Exercises - Page 502: 30


$ 24\pi x^{2}+72\pi x+54\pi$

Work Step by Step

$h=2r=2(2x+3)=4x+6$ $S.A.=2\pi r^{2}+2\pi rh$ ...surface area of a cylinder. $=2\pi(2x+3)^{2}+2\pi(2x+3)(4x+6)$ ...substitute $2x+3$ for $r $and $4x+6 $ for $h$. $=2\pi(2x+3)(2x+3)+2\pi(2x+3)(4x+6)$ ...write $(2x+3)^{2}$ as $(2x+3)(2x+3)$. $=2\pi(4x^{2}+6x+6x+9)+2\pi(8x^{2}+12x+12x+18)$ ...multiply binomials. $=2\pi(4x^{2}+12x+9)+2\pi(8x^{2}+24x+18)$ ...factor out $ 2\pi$. $=2\pi(4x^{2}+12x+9+8x^{2}+24x+18)$ ...combine like terms. $=2\pi(12x^{2}+36x+27)$ ...write in standard form. =$ 24\pi x^{2}+72\pi x+54\pi$
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