1. **State the problem:** Expand the expression $2x(3x^2 + 2x + 8)$. 2. **Recall the distributive property:** To expand, multiply $2x$ by each term inside the parentheses. 3. **Multiply each term:** $$2x \times 3x^2 = 6x^3$$ $$2x \times 2x = 4x^2$$ $$2x \times 8 = 16x$$ 4. **Write the expanded expression:** $$6x^3 + 4x^2 + 16x$$ 5. **Final answer:** The expanded form of $2x(3x^2 + 2x + 8)$ is $$6x^3 + 4x^2 + 16x$$