Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 5 Polynomials and Polynomial Functions - 5.4 Factor and Solve Polynomial Equations - 5.4 Exercises - Problem Solving - Page 359: 65c


See below.

Work Step by Step

We know that the sum of the three solids is $a^3-b^3$ from part a), but using part a), we can only sum them by summing their individual volumes, which gives us the equality: $a^3-b^3=a^2(a-b)+ab(a-b)+b^2(a-b)\\a^3-b^3=(a-b)(a^2+ab+b^2)$
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