## Elementary Algebra

$x+2\sqrt{x}-15$
Using $(a+b)(c+d)=ac+ad+bc+bd$, or the FOIL method, and the properties of radicals, the given expression, $(\sqrt{x}+5)(\sqrt{x}-3) ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{x}(\sqrt{x})+\sqrt{x}(-3)+5(\sqrt{x})+5(-3) \\\\= x-3\sqrt{x}+5\sqrt{x}-15 \\\\= x+2\sqrt{x}-15 .\end{array} Note that all variables represent positive real numbers.