Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 9 - Roots and Radicals - Chapter 9 Review Problem Set - Page 430: 44



Work Step by Step

Using $(a+b)(c+d)=ac+ad+bc+bd$, or the Distributive Property, and the properties of radicals, the given expression, $ (2\sqrt{3}+3\sqrt{2})(\sqrt{3}-5\sqrt{2}) ,$ simplifies to \begin{array}{l}\require{cancel} 2\sqrt{3}(\sqrt{3})+2\sqrt{3}(-5\sqrt{2})+3\sqrt{2}(\sqrt{3})+3\sqrt{2}(-5\sqrt{2}) \\\\= 2(3)-10\sqrt{6}+3\sqrt{6}-15(2) \\\\= 6-10\sqrt{6}+3\sqrt{6}-30 \\\\= (6-30)+(-10\sqrt{6}+3\sqrt{6}) \\\\= -24-7\sqrt{6} .\end{array}
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