1. **State the problem:** Multiply and simplify the expression $2x(x^2 - 8)$. Then name the simplified polynomial. 2. **Use the distributive property:** Multiply $2x$ by each term inside the parentheses. $$2x \cdot x^2 - 2x \cdot 8$$ 3. **Perform the multiplication:** $$2x^3 - 16x$$ 4. **Simplify the expression:** The polynomial is $2x^3 - 16x$. 5. **Name the polynomial:** - It has two terms, so it is a **binomial**. - The highest power of $x$ is 3, so it is a **cubic** polynomial. **Final answer:** The simplified polynomial is $2x^3 - 16x$, which is a cubic binomial.