To find the difference of the two expressions \( (9x^2 - 6x + ) - (x^2 + 4x - 39) \), we first need to clarify and ensure that the first expression is complete. Let's assume it meant to be \( 9x^2 - 6x + 0 \) for simplicity.
So we will compute:
\[ (9x^2 - 6x + 0) - (x^2 + 4x - 39) \]
Now, distribute the negative sign through the second expression:
\[ 9x^2 - 6x - x^2 - 4x + 39 \]
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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The constant term is \( +39\).
Putting it all together, we get:
\[ 8x^2 - 10x + 39 \]
Thus, the difference is:
\[ \boxed{8x^2 - 10x + 39} \]
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