## Intermediate Algebra (6th Edition)

$x-2\sqrt{x+1}+2$
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}