1. **State the problem:** Expand and simplify the expression $$3(5b - 2) - 4(3b + 5)$$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the factor outside. 3. **Apply the distributive property:** $$3 \times 5b = 15b$$ $$3 \times (-2) = -6$$ $$-4 \times 3b = -12b$$ $$-4 \times 5 = -20$$ 4. **Rewrite the expression with these products:** $$15b - 6 - 12b - 20$$ 5. **Combine like terms:** $$15b - 12b = 3b$$ $$-6 - 20 = -26$$ 6. **Final simplified expression:** $$3b - 26$$ This means the expanded and simplified form of the original expression is $$3b - 26$$.