Which example correctly demonstrates polynomial subtraction?

To correctly demonstrate polynomial subtraction for the expression \( (2x^2 + 6x + 1) - (3x^2 + 3x + 9) \), we need to distribute the negative sign to each term in the second polynomial and then combine like terms.

Let's perform the subtraction step by step:

1. Write the expression:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9)
\]

2. Distribute the negative sign:
\[
= 2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]

3. Now, 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: \( 1 - 9 = -8 \)

4. Putting it all together:
\[
-x^2 + 3x - 8
\]

Therefore, the correct answer is:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8
\]

So, the second option is correct:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8
\]