Answer
$\sqrt{35}+\sqrt{14}-\sqrt{10}-2$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$, or the product of 2 binomials, and the properties of radicals, the given expression, $
(\sqrt{7}-\sqrt{2})\sqrt{5}+\sqrt{2})
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt{7}(\sqrt{5})+\sqrt{7}(\sqrt{2})-\sqrt{2}(\sqrt{5})-\sqrt{2}(\sqrt{2})
\\\\=
\sqrt{7(5)}+\sqrt{7(2)}-\sqrt{2(5)}-\sqrt{(2)^2}
\\\\=
\sqrt{35}+\sqrt{14}-\sqrt{10}-2
.\end{array}
