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

Answer

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.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.