1. **State the problem:** Simplify the expression $$-y^2 + (-12) - 7y - (-5y^2) + 3y - 16$$. 2. **Recall the rules:** - Combine like terms: terms with the same variable and exponent. - Remember that subtracting a negative is the same as adding a positive. 3. **Rewrite the expression by removing unnecessary parentheses:** $$-y^2 - 12 - 7y + 5y^2 + 3y - 16$$ 4. **Group like terms:** - Quadratic terms: $$-y^2 + 5y^2$$ - Linear terms: $$-7y + 3y$$ - Constants: $$-12 - 16$$ 5. **Simplify each group:** - Quadratic: $$-y^2 + 5y^2 = (\cancel{-1} + 5) y^2 = 4y^2$$ - Linear: $$-7y + 3y = (-7 + 3) y = -4y$$ - Constants: $$-12 - 16 = -28$$ 6. **Write the simplified expression:** $$4y^2 - 4y - 28$$ **Final answer:** $$4y^2 - 4y - 28$$