To simplify the expression \((9x^2 - 6x + 2) - (x^2 + 4x - 39)\), follow these steps:
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Distribute the negative sign across the second polynomial: \[ (9x^2 - 6x + 2) - (x^2 + 4x - 39) = 9x^2 - 6x + 2 - x^2 - 4x + 39 \]
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Combine like terms:
- For the \(x^2\) terms: \(9x^2 - x^2 = 8x^2\)
- For the \(x\) terms: \(-6x - 4x = -10x\)
- For the constant terms: \(2 + 39 = 41\)
Putting it all together, we get: \[ 8x^2 - 10x + 41 \]
So, the simplified form of the difference of the polynomials is: \[ \boxed{8x^2 - 10x + 41} \]
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