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: 115

Answer

$x^{3}$ - 9$x^{2}$ + 27x - 27

Work Step by Step

$(x - 3)^{3}$ = (x - 3)(x - 3)(x - 3) = Remember that $(a-b)^{2}$ = $a^{2}$ - 2ab + $b^{2}$. So, (x - 3)(x - 3)(x - 3) = ($x^{2}$ - 2$\times$x$\times$3 + $3^{2}$)(x - 3) = ($x^{2}$ - 6x + 9)(x - 3) = Use the distributive property. $x^{2}$(x) +$x^{2}$(-3) -6x(x) -6x(-3) +9(x) +9(-3) = $x^{3}$ - 3$x^{2}$ - 6$x^{2}$ + 18x + 9x - 27 = Simplify. $x^{3}$ - 9$x^{2}$ + 27x - 27
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.