1. The problem is to simplify and evaluate the expression $$(\sqrt{7} - \sqrt{2})^2$$. 2. Recall the algebraic identity for the square of a binomial: $$ (a - b)^2 = a^2 - 2ab + b^2 $$. 3. Applying this formula with $a = \sqrt{7}$ and $b = \sqrt{2}$, we get: $$ (\sqrt{7} - \sqrt{2})^2 = (\sqrt{7})^2 - 2 \times \sqrt{7} \times \sqrt{2} + (\sqrt{2})^2 $$ 4. Simplify each term: - $(\sqrt{7})^2 = 7$ - $(\sqrt{2})^2 = 2$ - $2 \times \sqrt{7} \times \sqrt{2} = 2 \times \sqrt{14} = 2\sqrt{14}$ 5. Substitute back: $$ 7 - 2\sqrt{14} + 2 = 9 - 2\sqrt{14} $$ 6. Therefore, the simplified form of $$(\sqrt{7} - \sqrt{2})^2$$ is: $$ \boxed{9 - 2\sqrt{14}} $$ This is the exact simplified expression, combining like terms and applying the binomial square formula correctly.