1. **State the problem:** Simplify the expression $$(3u^2 - 3u + 8) - (5u^2 - 4u - 1) + (2u^2 + 3u + 4)$$. 2. **Remove parentheses carefully:** Remember to distribute the minus sign across the second parentheses. $$3u^2 - 3u + 8 - 5u^2 + 4u + 1 + 2u^2 + 3u + 4$$ 3. **Group like terms:** Group the $u^2$ terms, the $u$ terms, and the constant terms. $$ (3u^2 - 5u^2 + 2u^2) + (-3u + 4u + 3u) + (8 + 1 + 4) $$ 4. **Simplify each group:** $$ (3 - 5 + 2)u^2 + (-3 + 4 + 3)u + (8 + 1 + 4) $$ $$ 0u^2 + 4u + 13 $$ 5. **Final simplified expression:** $$4u + 13$$ This means the original expression simplifies to $4u + 13$.