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: 52

Answer

$\dfrac{6}{25}t^2-\dfrac{1}{5}t-1$

Work Step by Step

Using $(a+b)(c+d)=ac+ad+bc+bd$ or the product of $2$ binomials, the given expression, $ \left( \dfrac{2}{5}t-1 \right)\left( \dfrac{3}{5}t+1 \right) $, is equivalent to \begin{array}{l}\require{cancel} \dfrac{2}{5}t\left( \dfrac{3}{5}t \right)+\dfrac{2}{5}t(1)-1\left( \dfrac{3}{5}t \right)-1(1) \\\\= \dfrac{6}{25}t^2+\dfrac{2}{5}t-\dfrac{3}{5}t-1 \\\\= \dfrac{6}{25}t^2-\dfrac{1}{5}t-1 .\end{array}
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