1. **State the problem:** Simplify the expression $ax^{3} + ax^{2}$ without factoring. 2. **Recall the expression:** The given expression is $ax^{3} + ax^{2}$. 3. **Explain the terms:** Each term has a coefficient $a$ and powers of $x$. 4. **Simplify without factoring:** Since factoring is not allowed, we cannot take out common factors. 5. **Final expression:** The expression remains as $ax^{3} + ax^{2}$ because no further simplification without factoring is possible. **Answer:** $ax^{3} + ax^{2}$