To correctly demonstrate polynomial subtraction, we need to perform the operation step-by-step. Let's take the polynomial subtraction:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9)
\]
We can distribute the negative sign to the second polynomial:
\[
2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]
Now, combine like terms:
1. \(2x^2 - 3x^2 = -x^2\)
2. \(6x - 3x = 3x\)
3. \(1 - 9 = -8\)
Putting these together, we have:
\[
-x^2 + 3x - 8
\]
Now, let's compare this result with the given options:
1. \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -5x^2 + 3x - 8\) (incorrect)
2. \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8\) (correct)
3. \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = 5x^2 + 9x + 10\) (incorrect)
4. \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = x^2 + 3x + 8\) (incorrect)
The correct example that demonstrates polynomial subtraction is the second one:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8
\]