1. **State the problem:** Simplify the expression $$(3x^3 - 2x + x^2) - (x^2 + x^3)$$. 2. **Write down the expression clearly:** $$3x^3 - 2x + x^2 - x^2 - x^3$$ 3. **Combine like terms:** - Combine $3x^3$ and $-x^3$ to get $2x^3$. - Combine $x^2$ and $-x^2$ which cancel out to $0$. - The term $-2x$ remains as is. 4. **Simplified expression:** $$2x^3 - 2x$$ 5. **Factor if possible:** Factor out the common factor $2x$: $$2x(x^2 - 1)$$ 6. **Recognize difference of squares:** $$x^2 - 1 = (x - 1)(x + 1)$$ 7. **Final factored form:** $$2x(x - 1)(x + 1)$$ **Answer:** The simplified and factored form of the expression is $$2x(x - 1)(x + 1)$$.