\[\left( \sqrt{18} - \sqrt{2} \right)^{2} =\]
\[= \left( \sqrt{18} \right)^{2} - 2\sqrt{18} \cdot \sqrt{2} + \left( \sqrt{2} \right)^{2} =\]
\[= 18 - 2\sqrt{36} + 2 =\]
\[= 20 - 2 \cdot 6 = 20 - 12 = 8.\]