1. **State the problem:** Simplify the expression $4x(5x-20)$. 2. **Use the distributive property:** Multiply $4x$ by each term inside the parentheses. The distributive property states $a(b+c) = ab + ac$. 3. **Apply the property:** $$4x \times 5x = 20x^2$$ $$4x \times (-20) = -80x$$ 4. **Combine the results:** $$20x^2 - 80x$$ 5. **Factor if possible:** Factor out the common factor $20x$. $$20x(x - 4)$$ **Final answer:** $$20x(x - 4)$$