1. **State the problem:** Simplify the expression $b \times \frac{400 - b}{2}$. 2. **Write the expression:** The expression is $b \times \frac{400 - b}{2}$. 3. **Apply multiplication:** Multiply $b$ by each term inside the numerator: $$b \times \frac{400 - b}{2} = \frac{b \times 400 - b \times b}{2}$$ 4. **Simplify multiplication:** $$= \frac{400b - b^2}{2}$$ 5. **Final simplified form:** $$\frac{400b - b^2}{2}$$ This is the simplified form of the given expression, showing the product distributed and combined over the denominator 2.