1. **State the problem:** Expand and simplify the expression $$6y(5y + 4) - 5y(2y - 7)$$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the term outside. $$6y \times 5y = 30y^2$$ $$6y \times 4 = 24y$$ $$-5y \times 2y = -10y^2$$ $$-5y \times (-7) = +35y$$ 3. **Rewrite the expression with these products:** $$30y^2 + 24y - 10y^2 + 35y$$ 4. **Combine like terms:** Combine the $y^2$ terms: $$30y^2 - 10y^2 = 20y^2$$ Combine the $y$ terms: $$24y + 35y = 59y$$ 5. **Final simplified expression:** $$20y^2 + 59y$$