Question: Simplify. (-4v^2 + 8v + 2) + (5v^2 + 6v - 2) - (-8v^2 + 7v + 3)

Simplify. (-4v^2 + 8v + 2) + (5v^2 + 6v - 2) - (-8v^2 + 7v + 3)

Solution

To simplify the expression, combine like terms: Start with the expression: \[ (-4v^2 + 8v + 2) + (5v^2 + 6v - 2) - (8v^2 + 7v + 3) \] Distribute the negative sign through the third set of parentheses: \[ (-4v^2 + 8v + 2) + (5v^2 + 6v - 2) - 8v^2 - 7v - 3 \] Combine the \(v^2\) terms: \[ (-4v^2 + 5v^2 - 8v^2) = -7v^2 \] Combine the \(v\) terms: \[ (8v + 6v - 7v) = 7v \] Combine the constant terms: \[ (2 - 2 - 3) = -3 \] Write the simplified expression: \[ -7v^2 + 7v - 3 \]