1. **State the problem:** Simplify the expression $$(a^3 - 2a^2) - (3a^2 - 4a^3)$$. 2. **Apply the distributive property:** Remove the parentheses by distributing the minus sign over the second group: $$a^3 - 2a^2 - 3a^2 + 4a^3$$ 3. **Combine like terms:** Group the terms with $a^3$ and the terms with $a^2$: $$a^3 + 4a^3 - 2a^2 - 3a^2$$ 4. **Add coefficients:** $$ (1 + 4)a^3 - (2 + 3)a^2 = 5a^3 - 5a^2$$ 5. **Factor the expression:** Factor out the common factor $5a^2$: $$5a^2(a - 1)$$ **Final answer:** $$5a^2(a - 1)$$