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 10 - Exponents and Radicals - 10.5 Expressions Containing Several Radical Terms - 10.5 Exercise Set: 49

Answer

$2-8\sqrt{35}$

Work Step by Step

Using $(a+b)(c+d)=ac+ad+bc+bd$, or the product of 2 binomials, and the properties of radicals, the given expression, $ (3\sqrt{7}+2\sqrt{5})(2\sqrt{7}-4\sqrt{5}) ,$ is equivalent to \begin{array}{l}\require{cancel} (3\sqrt{7})(2\sqrt{7})+(3\sqrt{7})(-4\sqrt{5})+(2\sqrt{5})(2\sqrt{7})+(2\sqrt{5})(-4\sqrt{5}) \\\\= 6\sqrt{49}-12\sqrt{35}+4\sqrt{35}-8\sqrt{25} \\\\= 6\sqrt{(7)^2}-12\sqrt{35}+4\sqrt{35}-8\sqrt{(5)^2} \\\\= 6\cdot7-12\sqrt{35}+4\sqrt{35}-8\cdot5 \\\\= 42-12\sqrt{35}+4\sqrt{35}-40 \\\\= (42-40)+(-12\sqrt{35}+4\sqrt{35}) \\\\= 2-8\sqrt{35} .\end{array}
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