Let's simplify the expression \( (2x^2 + 6x + 1) - (3x^2 + 3x + 9) \).
-
Distribute the negative sign across the second polynomial: \[ (2x^2 + 6x + 1) - 3x^2 - 3x - 9 \]
-
Combine like terms:
- For the \(x^2\) terms: \(2x^2 - 3x^2 = -x^2\)
- For the \(x\) terms: \(6x - 3x = 3x\)
- For the constant terms: \(1 - 9 = -8\)
Putting it all together, we have: \[ -x^2 + 3x - 8 \]
Hence, the correct simplified expression is: \[ -x^2 + 3x - 8 \]
Looking at the options provided, the correct answer corresponds to: B. \((2x²+6x+1) - (3x²+3x+9) = -x²+3x-8\).