1. **Problem:** Simplify $\sqrt{2}(\sqrt{3}-\sqrt{2})^2$. 2. **Formula and rules:** Use the binomial expansion $(a-b)^2 = a^2 - 2ab + b^2$ and simplify radicals. 3. **Step-by-step:** $$ (\sqrt{3}-\sqrt{2})^2 = (\sqrt{3})^2 - 2\sqrt{3}\sqrt{2} + (\sqrt{2})^2 = 3 - 2\sqrt{6} + 2 $$ $$ = 5 - 2\sqrt{6} $$ Multiply by $\sqrt{2}$: $$ \sqrt{2}(5 - 2\sqrt{6}) = 5\sqrt{2} - 2\sqrt{2}\sqrt{6} $$ Simplify $\sqrt{2}\sqrt{6} = \sqrt{12} = 2\sqrt{3}$: $$ 5\sqrt{2} - 2 \times 2\sqrt{3} = 5\sqrt{2} - 4\sqrt{3} $$ **Final answer:** $5\sqrt{2} - 4\sqrt{3}$