1. **State the problem:** Simplify the expression $$(-x^2 - 4x + 1) - (2x^2 + 9)$$. 2. **Apply the subtraction:** Distribute the minus sign to the second polynomial: $$-x^2 - 4x + 1 - 2x^2 - 9$$ 3. **Combine like terms:** Group the terms with $$x^2$$, $$x$$, and constants: $$(-x^2 - 2x^2) + (-4x) + (1 - 9)$$ 4. **Simplify each group:** $$-x^2 - 2x^2 = -3x^2$$ $$1 - 9 = -8$$ So the expression becomes: $$-3x^2 - 4x - 8$$ 5. **Final answer:** $$\boxed{-3x^2 - 4x - 8}$$