1. **State the problem:** Multiply the expression $$\sqrt{5}(-7 + \sqrt{2})$$ and simplify the result. 2. **Distribute $$\sqrt{5}$$ to each term inside the parentheses:** $$\sqrt{5} \times (-7) + \sqrt{5} \times \sqrt{2}$$ 3. **Multiply each term:** - $$\sqrt{5} \times (-7) = -7\sqrt{5}$$ - $$\sqrt{5} \times \sqrt{2} = \sqrt{5 \times 2} = \sqrt{10}$$ 4. **Write the simplified expression:** $$-7\sqrt{5} + \sqrt{10}$$ This is the simplest form because $$\sqrt{5}$$ and $$\sqrt{10}$$ cannot be simplified further or combined. **Final answer:** $$-7\sqrt{5} + \sqrt{10}$$