1. **State the problem:** Expand and simplify the expression $$(3x-1)(x+7)$$. 2. **Apply the distributive property (FOIL method):** Multiply each term in the first parentheses by each term in the second parentheses. $$3x \cdot x + 3x \cdot 7 - 1 \cdot x - 1 \cdot 7$$ 3. **Calculate each product:** $$3x^2 + 21x - x - 7$$ 4. **Combine like terms:** $$3x^2 + (21x - x) - 7$$ $$3x^2 + 20x - 7$$ 5. **Final simplified expression:** $$3x^2 + 20x - 7$$