Simplify (9x^2 - 6x+ 2) - (x^2 + 4x - 39).

The difference of the polynomials is __

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To simplify the expression \((9x^2 - 6x + 2) - (x^2 + 4x - 39)\), we first distribute the negative sign through the second polynomial:

\[ (9x^2 - 6x + 2) - (x^2 + 4x - 39) = 9x^2 - 6x + 2 - x^2 - 4x + 39 \]

Now, we combine like terms:

  1. For the \(x^2\) terms: \[ 9x^2 - x^2 = 8x^2 \]

  2. For the \(x\) terms: \[ -6x - 4x = -10x \]

  3. For the constant terms: \[ 2 + 39 = 41 \]

Now, putting it all together, we have:

\[ 8x^2 - 10x + 41 \]

So, the simplified difference of the polynomials is:

\[ \boxed{8x^2 - 10x + 41} \]

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