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To correctly demonstrate polynomial subtraction, we need to subtract the second polynomial from the first and combine like terms appropriately. Let's break down the subtraction for the given example:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9)
\]
First, distribute the negative sign across the second polynomial:
\[
= 2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]
Now, combine like terms:
1. Combine the \(x^2\) terms: \(2x^2 - 3x^2 = -x^2\)
2. Combine the \(x\) terms: \(6x - 3x = 3x\)
3. Combine the constant terms: \(1 - 9 = -8\)
Putting it all together, we get:
\[
-x^2 + 3x - 8
\]
Thus, the correct answer is:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8
\]
So, the correct example demonstrating polynomial subtraction is:
**(2x² + 6x + 1) - (3x² + 3x + 9) = -x² + 3x - 8**.