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

$|x-4|$
Using the square of a binomial which is given by $(a+b)^2=a^2+2ab+b^2$ or by $(a-b)^2=a^2-2ab+b^2,$ the expression above is equivalent to \begin{array}{l}\require{cancel} \sqrt{x^2-8x+16} \\\\= \sqrt{(x-4)^2} .\end{array} Using $\sqrt[n]{x^n}=|x|$ if $n$ is even and $\sqrt[n]{x^n}=x$ if $n$ is odd, then \begin{array}{l}\require{cancel} \sqrt{(x-4)^2} \\\\= |x-4| .\end{array}