1. Stating the problem: Simplify the expression $$(\sqrt{7} - \sqrt{2})^{2}$$. 2. Recall the algebraic identity for the square of a difference: $$ (a - b)^2 = a^2 - 2ab + b^2 $$. 3. Assign $a = \sqrt{7}$ and $b = \sqrt{2}$. 4. Calculate each term: - $a^2 = (\sqrt{7})^2 = 7$ - $b^2 = (\sqrt{2})^2 = 2$ - $2ab = 2 \times \sqrt{7} \times \sqrt{2} = 2 \times \sqrt{14} = 2\sqrt{14}$ 5. Substitute back into the identity: $$ (\sqrt{7} - \sqrt{2})^{2} = 7 - 2\sqrt{14} + 2 $$ 6. Simplify the constants: $$ 7 + 2 = 9 $$ 7. Final expression: $$ 9 - 2\sqrt{14} $$ So, the simplified form is $$9 - 2\sqrt{14}$$.