1. **State the problem:** Simplify the expression $(4x^2 - 5x + 7) - (3x^2 + 2x - 5) + (2x^2 - x - 10)$. 2. **Write the expression clearly:** $$ (4x^2 - 5x + 7) - (3x^2 + 2x - 5) + (2x^2 - x - 10) $$ 3. **Distribute the minus signs:** $$ 4x^2 - 5x + 7 - 3x^2 - 2x + 5 + 2x^2 - x - 10 $$ 4. **Group like terms:** $$ (4x^2 - 3x^2 + 2x^2) + (-5x - 2x - x) + (7 + 5 - 10) $$ 5. **Simplify each group:** $$ (4 - 3 + 2)x^2 + (-5 - 2 - 1)x + (7 + 5 - 10) $$ $$ = 3x^2 - 8x + 2 $$ **Final answer:** $$ 3x^2 - 8x + 2 $$