1. **State the problem:** Simplify the expression $10x^2 - (x-2)x^2 - (x+8)$. 2. **Distribute and expand:** Apply the distributive property to the terms inside the parentheses: $$10x^2 - (x \cdot x^2 - 2 \cdot x^2) - (x + 8) = 10x^2 - (x^3 - 2x^2) - x - 8$$ 3. **Remove parentheses carefully:** Remember to distribute the minus sign to both terms inside the parentheses: $$10x^2 - x^3 + 2x^2 - x - 8$$ 4. **Combine like terms:** Group terms with the same powers of $x$: $$-x^3 + (10x^2 + 2x^2) - x - 8 = -x^3 + 12x^2 - x - 8$$ 5. **Final simplified expression:** $$\boxed{-x^3 + 12x^2 - x - 8}$$