Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - 10.8 The Complex Numbers - 10.8 Exercise Set: 100

Answer

$(t+10)(t^2-10t+100)$

Work Step by Step

The expressions $ t^3 $ and $ 1000 $ are both perfect cubes (the cube root is exact). Hence, $ t^3+1000 $ is a $\text{ sum }$ of $2$ cubes. Using the factoring of the sum or difference of $2$ cubes which is given by $a^3+b^3=(a+b)(a^2-ab+b^2)$ or by $a^3-b^3=(a-b)(a^2+ab+b^2)$ the expression above is equivalent to \begin{array}{l}\require{cancel} (t)^3+(10)^3 \\\\= (t+10)[(t)^2-t(10)+(10)^2] \\\\= (t+10)(t^2-10t+100) .\end{array}
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