To demonstrate the correct polynomial subtraction, we should follow the steps of distributing the negative sign and combining like terms. Let's start with the expression:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9)
\]
First, we distribute the negative sign to each term in the second polynomial:
\[
= 2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]
Now, we combine like terms:
- Combine the \(x^2\) terms: \(2x^2 - 3x^2 = -x^2\)
- Combine the \(x\) terms: \(6x - 3x = 3x\)
- Combine the constant terms: \(1 - 9 = -8\)
Putting it all together, we get:
\[
-x^2 + 3x - 8
\]
So, the correct answer from your provided responses is:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8
\]