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 - 8-4 Multiplying Soecial Cases - Practice and Problem-Solving Exercises - Page 509: 58


$V=\displaystyle \frac{4}{3}\pi x^{3}+12\pi x^{2}+36\pi x+36\pi $

Work Step by Step

$V=\displaystyle \frac{4}{3}\pi r^{3}$...the volume of a sphere with a radius r. $r=x+3$...substitute $x+3$ with $r $in the formula. $V=\displaystyle \frac{4}{3}\pi(x+3)^{3}$...write $(x+3)^{3}$ as $(x+3)^{2}\cdot(x+3)^{1}$. $V=\displaystyle \frac{4}{3}\pi(x+3)^{2}\cdot(x+3)$...square the binomial. $V=\displaystyle \frac{4}{3}\pi(x^{2}+2(x)(3)+3^{2})\cdot(x+3)$ ...simplify the first parentheses. $V=\displaystyle \frac{4}{3}\pi(x^{2}+6x+9)\cdot(x+3)$ ...distribute. $V=\displaystyle \frac{4}{3}\pi[(x^{2}+6x+9)\cdot x+(x^{2}+6x+9)\cdot 3]$ ...distribute. $V=\displaystyle \frac{4}{3}\pi(x^{3}+6x^{2}+9x+3x^{2}+18x+27)$ ...simplify. $V=\displaystyle \frac{4}{3}\pi(x^{3}+9x^{2}+27x+27)$ ...distribute. $V=\displaystyle \frac{4}{3}\pi x^{3}+12\pi x^{2}+36\pi x+36\pi $
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