Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 4 - Polynomials - 4.5 Multiplication of Polynomials - 4.5 Exercise Set: 50

Answer

$a^2+\dfrac{21}{10}a-1$

Work Step by Step

Using $(a+b)(c+d)=ac+ad+bc+bd$ or the product of $2$ binomials, the given expression, $ \left( a-\dfrac{2}{5} \right)\left( a+\dfrac{5}{2} \right) $, is equivalent to \begin{array}{l}\require{cancel} a(a)+a\left( \dfrac{5}{2} \right)-\dfrac{2}{5}(a)-\dfrac{2}{5}\left( \dfrac{5}{2} \right) \\\\= a^2+\dfrac{5}{2}a-\dfrac{2}{5}a-\dfrac{10}{10} \\\\= a^2+\dfrac{25}{10}a-\dfrac{4}{10}a-1 \\\\= a^2+\dfrac{21}{10}a-1 .\end{array}
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