Question: Simplify. (-4v^2 - 7v - 2) + (5v^2 + 5v + 7) - (9v^2 - 9v - 3)

Simplify. (-4v^2 - 7v - 2) + (5v^2 + 5v + 7) - (9v^2 - 9v - 3)

Solution

The problem is to simplify the expression: \[ (-4v^2 - 7v - 2) + (5v^2 + 5v + 7) - (9v^2 - 9v - 3) \] First, distribute the negative sign through the third expression: \[ -4v^2 - 7v - 2 + 5v^2 + 5v + 7 - 9v^2 + 9v + 3 \] Combine like terms: For \(v^2\) terms: \[ -4v^2 + 5v^2 - 9v^2 = (5 - 4 - 9)v^2 = -8v^2 \] For \(v\) terms: \[ -7v + 5v + 9v = (-7 + 5 + 9)v = 7v \] For constant terms: \[ -2 + 7 + 3 = 8 \] So, the simplified expression is: \[ -8v^2 + 7v + 8 \]