To subtract the polynomials \((3x - 5 - 7x^2) - (-2 + 6x^2 - 5x)\), we start by rewriting the expression without the parentheses. Remember to distribute the negative sign to each term in the second polynomial.
Original expression: \[ (3x - 5 - 7x^2) - (-2 + 6x^2 - 5x) \]
Step 1: Distribute the negative sign across the second set of parentheses: \[ 3x - 5 - 7x^2 + 2 - 6x^2 + 5x \]
Now, we combine like terms.
Step 2: Combine like terms:
- Combine the \(x^2\) terms: \(-7x^2 - 6x^2 = -13x^2\)
- Combine the \(x\) terms: \(3x + 5x = 8x\)
- Combine the constant terms: \(-5 + 2 = -3\)
The final combined expression is: \[ -13x^2 + 8x - 3 \]
So the final result of the subtraction of the two polynomials is: \[ -13x^2 + 8x - 3 \]