## Intermediate Algebra (12th Edition)

$6x+3\sqrt{x}-2\sqrt{5x}-\sqrt{5}$
$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $(3\sqrt{x}-\sqrt{5})(2\sqrt{x}+1) ,$ use FOIL and the laws of radicals. $\bf{\text{Solution Details:}}$ Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the expression above is equivalent to\begin{array}{l}\require{cancel} 3\sqrt{x}(2\sqrt{x})+3\sqrt{x}(1)-\sqrt{5}(2\sqrt{x})-\sqrt{5}(1) \\\\= 3(2)(\sqrt{x})^2+3\sqrt{x}-1(2)\sqrt{5}(\sqrt{x})-\sqrt{5} \\\\= 6x+3\sqrt{x}-2\sqrt{5}(\sqrt{x})-\sqrt{5} .\end{array} Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the expression above is equivalent to\begin{array}{l}\require{cancel} 6x+3\sqrt{x}-2\sqrt{5(x)}-\sqrt{5} \\\\= 6x+3\sqrt{x}-2\sqrt{5x}-\sqrt{5} .\end{array}