To simplify the expression \( (9x^2 - 6x) - (x^2 + 4x - 39) \), we will first distribute the negative sign and then combine like terms.
- Distributing the negative sign:
\[ (9x^2 - 6x) - (x^2 + 4x - 39) = 9x^2 - 6x - x^2 - 4x + 39 \]
- Combine the like terms:
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For the \( x^2 \) terms: \( 9x^2 - x^2 = 8x^2 \)
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For the \( x \) terms: \( -6x - 4x = -10x \)
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The constant term is \( +39 \).
Putting it all together:
\[ 8x^2 - 10x + 39 \]
Therefore, the simplified expression is:
\[ \boxed{8x^2 - 10x + 39} \]