To simplify the expression \((9x^2 + 17x + 13) - (2x^2 + 12x + 11)\), we start by distributing the negative sign to each term in the second parentheses:
\[ (9x^2 + 17x + 13) - (2x^2 + 12x + 11) = 9x^2 + 17x + 13 - 2x^2 - 12x - 11 \]
Now we can combine like terms:
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For the \(x^2\) terms: \[ 9x^2 - 2x^2 = 7x^2 \]
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For the \(x\) terms: \[ 17x - 12x = 5x \]
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For the constant terms: \[ 13 - 11 = 2 \]
Putting it all together, we have:
\[ 7x^2 + 5x + 2 \]
Thus, the expression simplifies to:
\(\boxed{7x^2 + 5x + 2}\)
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