To simplify the expression \((9x^2 - 6x + 2) - (x^2 + 4x - 39)\), you need to distribute the negative sign in front of the second polynomial and then combine like terms.
- Distribute the negative sign:
\[ (9x^2 - 6x + 2) - (x^2 + 4x - 39) = 9x^2 - 6x + 2 - x^2 - 4x + 39 \]
- Combine like terms:
- For \(x^2\) terms: \(9x^2 - x^2 = 8x^2\)
- For \(x\) terms: \(-6x - 4x = -10x\)
- For constant terms: \(2 + 39 = 41\)
So, the simplified expression is:
\[ 8x^2 - 10x + 41 \]
Therefore, the difference of the polynomials is:
\(\boxed{8x^2 - 10x + 41}\)
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