Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 5 - Exponents and Polynomials - 5.3 - Multiplying Polynomials - Problem Set 5.3: 117

Answer

8$n^{3}$ + 12$n^{2}$ + 6n + 1

Work Step by Step

$(2n + 1)^{3}$ = (2n + 1)(2n + 1)(2n + 1) = Remember that $(a+b)^{2}$ = $a^{2}$ + 2ab + $b^{2}$ So, (2n + 1)(2n + 1)(2n + 1) = [$(2n)^{2}$ + 2$\times$2n$\times$1 + $1^{2}$](2n + 1) = (4$n^{2}$ + 4n + 1)(2n + 1) = Use the distributive property. 4$n^{2}$(2n) +4$n^{2}$(1) +4n(2n) +4n(1) +1(2n) +1(1) = 8$n^{3}$ + 4$n^{2}$ + 8$n^{2}$ + 4n + 2n + 1 = Simplify. 8$n^{3}$ + 12$n^{2}$ + 6n + 1
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