Question: Simplify. (-4u^2 + 2u + 4) - (-u^2 - 5u - 9) + (-4u^2 - 6u - 5)

Simplify. (-4u^2 + 2u + 4) - (-u^2 - 5u - 9) + (-4u^2 - 6u - 5)

Solution

To simplify the expression \((-4u^2 + 2u + 4) - (-u^2 - 5u - 9) + (-4u^2 - 6u - 5)\), we will follow these steps: First, simplify inside each parentheses. Distribute the negative sign in the middle term: \[ (-4u^2 + 2u + 4) + (u^2 + 5u + 9) + (-4u^2 - 6u - 5) \] Next, combine like terms: Combine the \(u^2\) terms: \[ (-4u^2 + u^2 - 4u^2) = -7u^2 \] Combine the \(u\) terms: \[ (2u + 5u - 6u) = u \] Combine the constant terms: \[ (4 + 9 - 5) = 8 \] Thus, the simplified expression is: \[ -7u^2 + u + 8 \]