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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:
1. Combine the \(x^2\) terms:
\(9x^2 - x^2 = 8x^2\)
2. Combine the \(x\) terms:
\(-6x - 4x = -10x\)
3. Combine the constant terms:
\(2 + 39 = 41\)
Putting it all together, we have:
\[
8x^2 - 10x + 41
\]
So, the simplified expression is:
\[
\boxed{8x^2 - 10x + 41}
\]