1. **State the problem:** Simplify the expression $$(4b - 1)(3b - 7)$$. 2. **Use the distributive property (FOIL method):** Multiply each term in the first parenthesis by each term in the second. 3. **Calculate each product:** - First: $4b \times 3b = 12b^2$ - Outer: $4b \times (-7) = -28b$ - Inner: $-1 \times 3b = -3b$ - Last: $-1 \times (-7) = 7$ 4. **Combine all terms:** $$12b^2 - 28b - 3b + 7$$ 5. **Simplify like terms:** $$12b^2 - (28b + 3b) + 7 = 12b^2 - 31b + 7$$ 6. **Final answer:** $$\boxed{12b^2 - 31b + 7}$$