To simplify the expression \((9x^2 - 6x + 2) - (x^2 + 4x - 39)\), first distribute the negative sign through the second set of parentheses:
\[ 9x^2 - 6x + 2 - x^2 - 4x + 39 \]
Now, combine like terms:
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Combine the \(x^2\) terms: \(9x^2 - x^2 = 8x^2\)
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Combine the \(x\) terms: \(-6x - 4x = -10x\)
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Combine the constant terms: \(2 + 39 = 41\)
Putting it all together, we have:
\[ 8x^2 - 10x + 41 \]
So, the simplified expression is:
\[ \boxed{8x^2 - 10x + 41} \]
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