1. **State the problem:** Simplify the polynomial expression $$(-3x^2 + x) - (x^3 - 7x + 8)$$ by subtracting the second polynomial from the first. 2. **Write the expression clearly:** $$(-3x^2 + x) - (x^3 - 7x + 8)$$ 3. **Distribute the minus sign to the second polynomial:** $$-3x^2 + x - x^3 + 7x - 8$$ 4. **Rearrange terms in descending order of degree:** $$-x^3 - 3x^2 + (x + 7x) - 8$$ 5. **Combine like terms:** $$-x^3 - 3x^2 + 8x - 8$$ 6. **Final simplified polynomial:** $$-x^3 - 3x^2 + 8x - 8$$ --- 1. **State the problem:** Simplify the polynomial expression $$(x^3 - 6x^2 + 8) - (-x^2 + 3x - 4)$$ by subtracting the second polynomial from the first. 2. **Write the expression clearly:** $$x^3 - 6x^2 + 8 - (-x^2 + 3x - 4)$$ 3. **Distribute the minus sign to the second polynomial:** $$x^3 - 6x^2 + 8 + x^2 - 3x + 4$$ 4. **Rearrange terms in descending order of degree:** $$x^3 + (-6x^2 + x^2) - 3x + (8 + 4)$$ 5. **Combine like terms:** $$x^3 - 5x^2 - 3x + 12$$ 6. **Final simplified polynomial:** $$x^3 - 5x^2 - 3x + 12$$