1. **State the problem:** Simplify the expression $$(4r^3 + 3r^4) + (r^4 + 5r^3)$$ 2. **Identify like terms:** Terms with $r^4$ and terms with $r^3$ can be combined. 3. **Group like terms:** $$4r^3 + 5r^3 + 3r^4 + r^4$$ 4. **Add coefficients of like terms:** $$ (4 + 5)r^3 + (3 + 1)r^4 = 9r^3 + 4r^4$$ 5. **Rewrite in standard form (descending powers):** $$4r^4 + 9r^3$$ 6. **Compare with given answer:** The boxed answer is $2r^4 + 9r^3$, which is incorrect because $3r^4 + r^4 = 4r^4$, not $2r^4$. **Final answer:** $$\boxed{4r^4 + 9r^3}$$