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To complete the polynomial equation that involves the subtraction of the second expression from the first, we need to structure it properly.
Given the first expression:
\[ 9x^2 + 2x + 13 \]
And the second expression:
\[ 2x^2 + 12x + 2 \]
We now need to subtract the second expression from the first:
\[
(9x^2 + 2x + 13) - (2x^2 + 12x + 2)
\]
Distributing the negative sign across the second polynomial yields:
\[
9x^2 + 2x + 13 - 2x^2 - 12x - 2
\]
Now, let's combine like terms:
1. For \(x^2\) terms: \(9x^2 - 2x^2 = 7x^2\)
2. For \(x\) terms: \(2x - 12x = -10x\)
3. For constant terms: \(13 - 2 = 11\)
Putting it all together, the resulting difference is:
\[
7x^2 - 10x + 11
\]
So, the completed polynomial equation showing the subtraction is:
\[
9x^2 + 2x + 13 - (2x^2 + 12x + 2) = 7x^2 - 10x + 11
\]