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 5.3 - Special Products - Exercise Set: 82

Answer

$\dfrac{3}{16}x^4+11x^2-64$

Work Step by Step

Using $(a+b)(c+d)=ab+ad+bc+bd$ or the FOIL Method, the product of the given expression, $ \left( \dfrac{1}{4}x^2+16 \right)\left( \dfrac{3}{4}x^2-4 \right) ,$ is \begin{array}{l}\require{cancel} \dfrac{1}{4}x^2\left( \dfrac{3}{4}x^2 \right)+\dfrac{1}{4}x^2(-4)+16\left(\dfrac{3}{4}x^2\right)+16(-4) \\\\= \dfrac{3}{16}x^4-x^2+12x^2-64 \\\\= \dfrac{3}{16}x^4+11x^2-64 .\end{array}
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