1. **State the problem:** Distribute and simplify the expression $$(x - 7)(x - 3)$$. 2. **Recall the distributive property (FOIL method):** $$(a - b)(c - d) = ac - ad - bc + bd$$ 3. **Apply FOIL to the given expression:** $$x \cdot x - x \cdot 3 - 7 \cdot x + 7 \cdot 3$$ 4. **Calculate each term:** $$x^2 - 3x - 7x + 21$$ 5. **Combine like terms:** $$x^2 - (3x + 7x) + 21 = x^2 - 10x + 21$$ 6. **Final simplified expression:** $$x^2 - 10x + 21$$ 7. **Match with the given options:** Option A is $$x^2 + (-10x) + 21$$ which is equivalent to $$x^2 - 10x + 21$$. **Answer:** A