College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.4: 94


The volume of the rectangular solid is $4x^3-26x^2+40x$ cubic units.

Work Step by Step

The formula for the volume of a rectangular solid is $v=lwh$ (volume equals length times width times height. This solid has the dimensions $8-2x$ by $5-2x$ by $x$. $$v=(8-2x)(5-2x)(x)$$ $$v=[(8\times 5)+(8\times (-2x))+(-2x\times 5)+(-2x\times (-2x))](x)$$ $$v=(40-16x-10x+4x^2)(x)$$ $$v=(40-26x+4x^2)(x)$$ $$v=(40\times x)+(-26x\times x)+(4x^2\times x)$$ $$v=40x-26x^2+4x^3$$ In standard notation, list the terms in order from highest degree to lowest degree: $$v=4x^3-26x^2+40x$$ The volume is $4x^3-26x^2+40x$ cubic units.
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