Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Section 7.4 - Adding, Subtracting, and Multiplying Radical Expressions - Exercise Set - Page 439: 61

Answer

$-16-\sqrt[]{35}$

Work Step by Step

Using $(a+b)(c+d)=ac+ad+bc+bd$ or the FOIL method, then, \begin{array}{l} \left( 2\sqrt[]{7}+3\sqrt[]{5} \right)\left( \sqrt[]{7}-2\sqrt[]{5} \right) \\= (2\sqrt[]{7})(\sqrt[]{7})+(2\sqrt[]{7})(-2\sqrt[]{5})+(3\sqrt[]{5})(\sqrt[]{7})+(3\sqrt[]{5})(-2\sqrt[]{5}) \\= 2\sqrt[]{49}-4\sqrt[]{35}+3\sqrt[]{35}-6\sqrt[]{25} \\= 2\cdot7-\sqrt[]{35}-6\cdot5 \\= 14-\sqrt[]{35}-30 \\= -16-\sqrt[]{35} .\end{array}
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