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: 120

Answer

64$n^{3}$ - 144$n^{2}$ + 108n - 27

Work Step by Step

$(4n - 3)^{3}$ = (4n - 3)(4n - 3)(4n - 3) = Remember that $(a-b)^{2}$ = $a^{2}$ - 2ab + $b^{2}$. So, (4n - 3)(4n - 3)(4n - 3) = [$(4n)^{2}$ - 2$\times$4n$\times$3 + $3^{2}$](4n - 3) = (16$n^{2}$ - 24n + 9)(4n - 3) = Use the distributive property. 16$n^{2}$(4n) +16$n^{2}$(-3) -24n(4n) -24n(-3) +9(4n) +9(-3) = 64$n^{3}$ - 48$n^{2}$ - 96$n^{2}$ + 72n + 36n - 27 Simplify. 64$n^{3}$ - 144$n^{2}$ + 108n - 27
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