Answer
$y-6\sqrt{2y}-14$
Work Step by Step
Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the given expression, $
(\sqrt{y}+\sqrt{2})(\sqrt{y}-7\sqrt{2})
,$ is equivalent to
\begin{align*}
&
\sqrt{y}(\sqrt{y})+\sqrt{y}(-7\sqrt{2})+\sqrt{2}(\sqrt{y})+\sqrt{2}(-7\sqrt{2})
\\&=
(\sqrt{y})^2-7\sqrt{2(y)}+\sqrt{2(y)}-7(\sqrt{2})^2
\\&=
y-7\sqrt{2y}+\sqrt{2y}-7(2)
\\&=
y-7\sqrt{2y}+\sqrt{2y}-14
\\&=
y+(-7\sqrt{2y}+\sqrt{2y})-14
\\&=
y-6\sqrt{2y}-14
.\end{align*}
Hence, the simplified form of the given expression is $
y-6\sqrt{2y}-14
$.
