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: 114

Answer

$x^{3}$ + 12$x^{2}$ + 48x + 64

Work Step by Step

$(x + 4)^{3}$ = (x + 4)(x + 4)(x + 4) = Remember that $(a+b)^{2}$ = $a^{2}$ + 2ab + $b^{2}$ So, (x + 4)(x + 4)(x + 4) = ($x^{2}$ + 2$\times$x$\times$4 + $4^{2}$)(x + 4) = ($x^{2}$ + 8x + 16)(x + 4) = Use the distributive property. $x^{2}$(x) + $x^{2}$(4) +8x(x) +8x(4) +16(x) +16(4) = $x^{3}$ + 4$x^{2}$ + 8$x^{2}$ + 32x + 16x + 64 = Simplify. $x^{3}$ + 12$x^{2}$ + 48x + 64
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