1. **State the problem:** Simplify the expression $x[x^2 + 3]$. 2. **Recall the distributive property:** For any numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. 3. **Apply the distributive property:** $$x[x^2 + 3] = x \cdot x^2 + x \cdot 3$$ 4. **Simplify each term:** $$x \cdot x^2 = x^{1+2} = x^3$$ $$x \cdot 3 = 3x$$ 5. **Write the final simplified expression:** $$x^3 + 3x$$ This is the simplified form of the original expression.