To simplify the expression \( (9x^2 - 6x + 2) - (x^2 + 4x - 39) \), we need to distribute the negative sign across the second polynomial and then combine like terms. Here’s the step-by-step solution:
-
Rewrite the expression: \[ 9x^2 - 6x + 2 - (x^2 + 4x - 39) \]
-
Distribute the negative sign: \[ 9x^2 - 6x + 2 - x^2 - 4x + 39 \]
-
Combine like terms:
- For the \(x^2\) terms: \[ 9x^2 - x^2 = 8x^2 \]
- For the \(x\) terms: \[ -6x - 4x = -10x \]
- For the constant terms: \[ 2 + 39 = 41 \]
-
Putting it all together, we get: \[ 8x^2 - 10x + 41 \]
So, the simplified expression is: \[ \boxed{8x^2 - 10x + 41} \]
1 answer