1. **State the problem:** Simplify the expression $25 - (x + 3 - x^2)$. 2. **Apply the distributive property:** When subtracting a group of terms inside parentheses, distribute the negative sign to each term inside. $$25 - (x + 3 - x^2) = 25 - x - 3 + x^2$$ 3. **Combine like terms:** Group the terms by their degree and combine constants. $$25 - 3 = 22$$ So the expression becomes $$x^2 - x + 22$$ 4. **Check for errors:** The original expression was simplified correctly. The mistake in the user's last step was dropping the $x^2$ term and incorrectly writing $x + 22$ instead of $x^2 - x + 22$. 5. **Answer:** The correct simplified expression is $$\boxed{x^2 - x + 22}$$ 6. **Identify the error type:** The error corresponds to option C: confusing negative signs when adding and subtracting terms.