Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.3 - Algebraic Expressions - 1.3 Exercises - Page 34: 79

Answer

$27x^{3}+y^{3}=(3x+y)(9x^{2}-3xy+y^{2})$

Work Step by Step

$27x^{3}+y^{3}$ This is a sum of cubes. The formula for factoring an expression in this form is $A^{3}+B^{3}=(A+B)(A^{2}-AB+B^{2})$. For this expression, $A^{3}=27x^{3}$ and $B^{3}=y^{3}$. Factor using the formula: $27x^{3}+y^{3}=(3x+y)(9x^{2}-3xy+y^{2})$
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