Question: Subtract $-2x^2 + 3x - 9$ from $6x^2 - 4x + 4$. The difference is $\boxed{}$. (Simplify your…

Subtract $-2x^2 + 3x - 9$ from $6x^2 - 4x + 4$.

The difference is $\boxed{}$. (Simplify your answer.)

Solution

To solve the problem, we need to subtract the polynomial \( -2x^2 + 3x - 9 \) from \( 6x^2 - 4x + 4 \). First, set up the expression for subtraction: \[ (6x^2 - 4x + 4) - (-2x^2 + 3x - 9) \] Distribute the negative sign across the second polynomial: \[ 6x^2 - 4x + 4 + 2x^2 - 3x + 9 \] Combine like terms: - Combine the \(x^2\) terms: \(6x^2 + 2x^2 = 8x^2\) - Combine the \(x\) terms: \(-4x - 3x = -7x\) - Combine the constant terms: \(4 + 9 = 13\) Thus, the simplified expression is: \[ 8x^2 - 7x + 13 \]