1. **Stating the problem:** Simplify the expression $$(\sqrt{2} - \sqrt{3})(\sqrt{2} + \sqrt{3}) - 2(\sqrt{2} + \sqrt{3})$$. 2. **Simplify the first product using the difference of squares formula:** $$ (\sqrt{2} - \sqrt{3})(\sqrt{2} + \sqrt{3}) = (\sqrt{2})^2 - (\sqrt{3})^2 = 2 - 3 = -1 $$ 3. **Rewrite the expression with the simplified product:** $$ -1 - 2(\sqrt{2} + \sqrt{3}) $$ 4. **Distribute the -2 across the terms inside the parentheses:** $$ -1 - 2\sqrt{2} - 2\sqrt{3} $$ 5. **Final simplified form:** $$ -1 - 2\sqrt{2} - 2\sqrt{3} $$ This is the simplest form; no like terms to combine further.