1. **State the problem:** Simplify the expression $$6y(5y + 4) - 5y(2y - 7)$$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the term outside. 3. **Calculate each part:** - $$6y \times 5y = 30y^2$$ - $$6y \times 4 = 24y$$ - $$-5y \times 2y = -10y^2$$ - $$-5y \times (-7) = +35y$$ 4. **Rewrite the expression:** $$30y^2 + 24y - 10y^2 + 35y$$ 5. **Combine like terms:** - Combine $$30y^2$$ and $$-10y^2$$ to get $$20y^2$$ - Combine $$24y$$ and $$35y$$ to get $$59y$$ 6. **Final simplified expression:** $$20y^2 + 59y$$ This is the simplified form of the given expression.