To correctly demonstrate polynomial subtraction, we need to perform the subtraction step by step.
Let's break down the expression \((2x^2 + 6x + 1) - (3x^2 + 3x + 9)\):
1. **Distribute the negative sign** to the second polynomial:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = 2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]
2. **Combine like terms**:
- For \(x^2\) terms: \(2x^2 - 3x^2 = -1x^2\)
- For \(x\) terms: \(6x - 3x = 3x\)
- For constant terms: \(1 - 9 = -8\)
Putting it all together, we get:
\[
-1x^2 + 3x - 8
\]
Thus, the correct equivalent expression for the subtraction is:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8
\]
So, the correct answer from the provided options is:
\((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8\).