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: 29


$ 4\pi x^{2}+22\pi x+28\pi$

Work Step by Step

$(x+2)$- radius of the cylinder $(x+5)$-height of the cylinder $S.A.=2\pi r^{2}+2\pi rh$ ...surface area of a cylinder. $=2\pi(x+2)^{2}+2\pi(x+2)(x+5)$ ...substitute $x+2$ for $r $ and $x+5 $for $h$. $=2\pi(x+2)(x+2)+2\pi(x+2)(x+5)$ ...write $(x+2)^{2}$ as $(x+2)(x+2)$. $=2\pi(x^{2}+2x+2x+4)+2\pi(x^{2}+5x+2x+10)$ ...multiply binomials. $=2\pi(x^{2}+4x+4)+2\pi(x^{2}+7x+10)$ ...factor out $ 2\pi$. $=2\pi(x^{2}+4x+4+x^{2}+7x+10)$ ...combine like terms. $=2\pi(2x^{2}+11x+14)$ ...write in standard form. =$ 4\pi x^{2}+22\pi x+28\pi$
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