Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 5 - Section 5.2 - Multiplying Polynomials - Exercise Set: 74

Answer

$x^4+5x^3+11x^2+10x+3$

Work Step by Step

Using the Distributive Property, the given expression, $ (x+1)(x^3+4x^2+7x+3) ,$ is equivalent to \begin{array}{l}\require{cancel} x(x^3)+x(4x^2)+x(7x)+x(3)+1(x^3)+1(4x^2)+1(7x)+1(3) \\\\= x^4+4x^3+7x^2+3x+x^3+4x^2+7x+3 \\\\= x^4+(4x^3+x^3)+(7x^2+4x^2)+(3x+7x)+3 \\\\= x^4+5x^3+11x^2+10x+3 .\end{array}
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