Question: Simplify. (-7y^2 + 8y - 1) - (2y^2 - 6y + 9) + (-5y^2 + 7y - 6)

Simplify. (-7y^2 + 8y - 1) - (2y^2 - 6y + 9) + (-5y^2 + 7y - 6)

Solution

To simplify the given expression, follow these steps: The expression is: \[ (-7y^2 + 8y - 1) - (2y^2 - 6y + 9) + (-5y^2 + 7y - 6) \] First, distribute the negative signs: \[ -7y^2 + 8y - 1 - 2y^2 + 6y - 9 - 5y^2 + 7y - 6 \] Combine like terms: 1. Combine the \(y^2\) terms: \[ (-7y^2 - 2y^2 - 5y^2) = -14y^2 \] 2. Combine the \(y\) terms: \[ (8y + 6y + 7y) = 21y \] 3. Combine the constant terms: \[ (-1 - 9 - 6) = -16 \] So the simplified expression is: \[ -14y^2 + 21y - 16 \]