Answer
$\sqrt{2}(\sqrt{2}+x\sqrt{6})=2x\sqrt{3}+2$
Work Step by Step
$\sqrt{2}(\sqrt{2}+x\sqrt{6})$
Evaluate the product:
$\sqrt{2}(\sqrt{2}+x\sqrt{6})=\sqrt{2^{2}}+x\sqrt{12}=...$
Rewrite the expression as $\sqrt{2^{2}}+x\sqrt{4\cdot3}$ and simplify:
$...=\sqrt{2^{2}}+x\sqrt{4\cdot3}=2x\sqrt{3}+2$