1. **State the problem:** Simplify the expression $ax^3 + ax^2$. 2. **Formula and rules:** To simplify expressions like this, we use the distributive property: $a(b + c) = ab + ac$. 3. **Apply the distributive property:** Factor out the common term $ax^2$ from both terms: $$ax^3 + ax^2 = ax^2(x) + ax^2(1) = ax^2(x + 1)$$ 4. **Final simplified form:** $$ax^3 + ax^2 = ax^2(x + 1)$$ This means the expression is factored by taking out the greatest common factor $ax^2$, leaving the sum inside the parentheses.