1. The problem is to simplify the expression $ (4y - y^2) + (4y^2 + y) $. 2. We use the rule of combining like terms: terms with the same variable and exponent can be added or subtracted. 3. Group like terms: $$ (4y - y^2) + (4y^2 + y) = 4y - y^2 + 4y^2 + y $$ 4. Combine like terms: - Combine $4y$ and $y$ to get $5y$. - Combine $-y^2$ and $4y^2$ to get $3y^2$. 5. So the simplified expression is: $$ 3y^2 + 5y $$ This is the final simplified form of the given expression.