## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$x+8\sqrt{x-3}+13$
Using $(a+b)^2=a^2+2ab+b^2$, or the square of a binomial, and the properties of radicals, the given expression, $(4+\sqrt{x-3})^2 ,$ is equivalent to \begin{array}{l}\require{cancel} (4)^2+2(4)(\sqrt{x-3})+(\sqrt{x-3})^2 \\\\= 16+8\sqrt{x-3}+x-3 \\\\= x+8\sqrt{x-3}+(-3+16) \\\\= x+8\sqrt{x-3}+13 .\end{array}