To simplify the expression \((9x^2 - 6x + 2) - (x^2 + 4x - 39)\), we can follow these steps:
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Distribute the negative sign across the terms in the second parentheses: \[ (9x^2 - 6x + 2) - x^2 - 4x + 39 \]
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Combine like terms:
- Combine \(9x^2\) and \(-x^2\): \[ 9x^2 - x^2 = 8x^2 \]
- Combine \(-6x\) and \(-4x\): \[ -6x - 4x = -10x \]
- Combine the constants \(2\) and \(39\): \[ 2 + 39 = 41 \]
Putting it all together, we get: \[ 8x^2 - 10x + 41 \]
So, the simplified expression is: \[ \boxed{8x^2 - 10x + 41} \]
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