1. **State the problem:** Add the polynomials $ (3x^2 - 5y^2 + 2y) + (8y^2 - 4y - 7x^2) $. 2. **Write the expression:** $$ (3x^2 - 5y^2 + 2y) + (8y^2 - 4y - 7x^2) $$ 3. **Group like terms:** $$ (3x^2 - 7x^2) + (-5y^2 + 8y^2) + (2y - 4y) $$ 4. **Simplify each group:** - For $x^2$ terms: $$ 3x^2 - 7x^2 = \cancel{3x^2} - 7x^2 = -4x^2 $$ - For $y^2$ terms: $$ -5y^2 + 8y^2 = \cancel{-5y^2} + 8y^2 = 3y^2 $$ - For $y$ terms: $$ 2y - 4y = \cancel{2y} - 4y = -2y $$ 5. **Write the final simplified polynomial:** $$ -4x^2 + 3y^2 - 2y $$ **Answer:** The sum of the polynomials is $-4x^2 + 3y^2 - 2y$.