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: 49

Answer

$t^2+\dfrac{17}{6}t+2$

Work Step by Step

Using $(a+b)(c+d)=ac+ad+bc+bd$ or the product of $2$ binomials, the given expression, $ \left( t+\dfrac{3}{2} \right)\left( t+\dfrac{4}{3} \right) $, is equivalent to \begin{array}{l}\require{cancel} t(t)+t\left( \dfrac{4}{3} \right)+\dfrac{3}{2}(t)+\dfrac{3}{2}\left( \dfrac{4}{3} \right) \\\\= t^2+\dfrac{4}{3}t+\dfrac{3}{2}t+\dfrac{12}{6} \\\\= t^2+\dfrac{8}{6}t+\dfrac{9}{6}t+2 \\\\= t^2+\dfrac{17}{6}t+2 .\end{array}
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