Answer
$2x\sqrt{3}-2\sqrt{6xy}$
Work Step by Step
Using $a(b+c)=ab+ac$, or the Distributive Property, and the properties of radicals, the given expression, $
\sqrt{6x}(\sqrt{2x}-\sqrt{4y})
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt{6x}(\sqrt{2x})-\sqrt{6x}(\sqrt{4y})
\\\\=
\sqrt{12x^2}-\sqrt{24xy}
\\\\=
\sqrt{4x^2\cdot3}-\sqrt{4\cdot6xy}
\\\\=
\sqrt{(2x)^2\cdot3}-\sqrt{(2)^2\cdot6xy}
\\\\=
2x\sqrt{3}-2\sqrt{6xy}
.\end{array}
Note that all variables represent positive real numbers.
