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

Solution

Simplify the expression: \[ (-8y^2 + 7) + (-2y^2 - 2y - 2) - (5y^2 - 2y - 7) \] Distribute the negative sign into the third group: \[ (-8y^2 + 7) + (-2y^2 - 2y - 2) - 5y^2 + 2y + 7 \] Combine like terms: Combine the \(y^2\) terms: \[ -8y^2 - 2y^2 - 5y^2 = -15y^2 \] Combine the \(y\) terms: \[ -2y + 2y = 0 \] Combine the constant terms: \[ 7 - 2 + 7 = 12 \] The simplified expression is: \[ -15y^2 + 12 \]