1. **State the problem:** Multiply and simplify the expression $-2x (x^2 - 8)$ and then name the simplified polynomial. 2. **Use the distributive property:** Multiply $-2x$ by each term inside the parentheses: $$-2x \cdot x^2 = -2x^3$$ $$-2x \cdot (-8) = +16x$$ 3. **Write the simplified polynomial:** $$-2x^3 + 16x$$ 4. **Name the polynomial:** - The highest power of $x$ is 3, so it is a **cubic** polynomial. - There are two terms, so it is a **binomial**. **Final answer:** The simplified polynomial is $$-2x^3 + 16x$$ and it is called a **cubic binomial**.