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: 65

Answer

$\dfrac{3}{16}x^2+\dfrac{11}{4}x-4$

Work Step by Step

Using $(a+b)(c+d)=ac+ad+bc+bd$ or the Distributive Property, the given expression, $ \left( \dfrac{1}{4}x+4 \right)\left( \dfrac{3}{4}x-1 \right) ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{1}{4}x\left( \dfrac{3}{4}x \right)+\dfrac{1}{4}x(-1)+4\left( \dfrac{3}{4}x \right)+4(-1) \\\\= \dfrac{3}{16}x^2-\dfrac{1}{4}x+\dfrac{12}{4}x-4 \\\\= \dfrac{3}{16}x^2+\dfrac{11}{4}x-4 .\end{array}
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