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 440: 90

Answer

$8-2\sqrt{10}+2\sqrt{5}-2\sqrt{2}$

Work Step by Step

Using $(a+b+c)=a^2+b^2+c^2+2ab+2ac+2bc$ (or the square of a multinomial), the given expression, $ (\sqrt{5}-\sqrt{2}+1)^2 ,$ is equivalent to \begin{array}{l}\require{cancel} (\sqrt{5})^2+(-\sqrt{2})^2+(1)^2+2(\sqrt{5})(-\sqrt{2})+2(\sqrt{5})(1)+2(-\sqrt{2})(1) \\\\= 5+2+1-2\sqrt{5(2)}+2\sqrt{5}-2\sqrt{2} \\\\= 8-2\sqrt{10}+2\sqrt{5}-2\sqrt{2} .\end{array}
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