Intermediate Algebra (6th Edition)

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

Chapter 7 - Sections 7.1-7.5 - Integrated Review - Radicals and Rational Exponents - Page 447: 34



Work Step by Step

Using $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, the given expression, $ \left( \sqrt{x+1}-1 \right)^2 ,$ is equivalent to \begin{array}{l}\require{cancel} (\sqrt{x+1})^2+2(\sqrt{x+1})(-1)+(-1)^2 \\\\= x+1-2\sqrt{x+1}+1 \\\\= x-2\sqrt{x+1}+2 .\end{array}
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