Answer
$14+7\sqrt2$
Work Step by Step
Recall:
$(a+b)(c+d) = a(c+d) + b(c+d)$
Use the rule above to obtain:
\begin{align*}
&=3(4+\sqrt2) +\sqrt2(4+\sqrt2)\\
&=3(4)+3(\sqrt2)+\sqrt2(4)+\sqrt2(\sqrt2)\\
&=12+3\sqrt2+4\sqrt2+\sqrt4\\
&=12+3\sqrt2+4\sqrt2+2\\
&=14+3\sqrt2+4\sqrt2
\end{align*}
Combine like terms to obtain:
\begin{align*}
&=14+(3+4)(\sqrt2)\\
&=14+7\sqrt2
\end{align*}
