To simplify the given polynomial expression:
\[ (3x - 5 - 7x^2) - (-2 + 6x^2 - 5x) \]
we need to first distribute the negative sign across the second polynomial:
\[ (3x - 5 - 7x^2) + (2 - 6x^2 + 5x) \]
Now, we can combine like terms. First, let's group the terms by their degrees:
- For \(x^2\) terms: \(-7x^2 + (-6x^2) = -7x^2 - 6x^2 = -13x^2\)
- For \(x\) terms: \(3x + 5x = 8x\)
- For constant terms: \(-5 + 2 = -3\)
Putting it all together, we combine the results:
\[ -13x^2 + 8x - 3 \]
Thus, the simplified form of the polynomial is:
\[ -13x^2 + 8x - 3 \]