Answer
$\sqrt{39}+\sqrt{143}-\sqrt{21}-\sqrt{77}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
(\sqrt{13}-\sqrt{7})(\sqrt{3}+\sqrt{11})
,$ use FOIL and the properties 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}
\sqrt{13}(\sqrt{3})+\sqrt{13}(\sqrt{11})-\sqrt{7}(\sqrt{3})-\sqrt{7}(\sqrt{11})
.\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}
\sqrt{13(3)}+\sqrt{13(11)}-\sqrt{7(3)}-\sqrt{7(11)}
\\\\=
\sqrt{39}+\sqrt{143}-\sqrt{21}-\sqrt{77}
.\end{array}
