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: 119

Answer

27$n^{3}$ - 54$n^{2}$ + 36n - 8

Work Step by Step

$(3n - 2)^{3}$ = (3n - 2)(3n - 2)(3n - 2) = Remember that $(a-b)^{2}$ = $a^{2}$ - 2ab + $b^{2}$. So, (3n - 2)(3n - 2)(3n - 2) = [$(3n)^{2}$ - 2$\times$3n$\times$2 + $2^{2}$](3n - 2) = (9$n^{2}$ - 12n + 4)(3n - 2) = Use the distributive property. 9$n^{2}$(3n) +9$n^{2}$(-2) -12n(3n) -12n(-2) +4(3n) +4(-2) = 27$n^{3}$ - 18$n^{2}$ - 36$n^{2}$ + 24n + 12n - 8 = 27$n^{3}$ - 54$n^{2}$ + 36n - 8
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