Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 5 - Exponents and Polynomials - Chapter 5 Review Problem Set: 36

Answer

$2x^3+7x^2+10x-7$

Work Step by Step

RECALL: The distributive property states that for any real numbers a, b, and c: $a(b+c) = ab+ac \\a(b-c) = ab - ac$ Use the distributive property (which is shown above) to obtain: $=2x(x^2+4x+7)-1(x^2+4x+7) \\=2x(x^2)+2x(4x)+2x(7)-1(x^2) -1(4x)-1(7) \\=2x^3+8x^2+14x-x^2-4x-7$ Combine like terms to obtain: $=2x^3+(8x^2-x^2)+(14x-4x)-7 \\=2x^3+7x^2+10x-7$
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