1. **State the problem:** Match each algebraic expression to its corresponding graph or simplified form. 2. **Expressions given:** - $x(x - 4)$ - $4x(x + 1)$ - $-4x^2 - 2x + 5$ 3. **Simplify each expression:** - For $x(x - 4)$, use distributive property: $$x(x - 4) = x^2 - 4x$$ - For $4x(x + 1)$, distribute $4x$: $$4x(x + 1) = 4x^2 + 4x$$ - The third expression is already simplified: $-4x^2 - 2x + 5$ 4. **Summary of simplified forms:** - $x^2 - 4x$ - $4x^2 + 4x$ - $-4x^2 - 2x + 5$ 5. **Explanation:** Each expression is a quadratic polynomial. The first two are factored forms expanded to standard form. The third is already in standard form. 6. **Matching:** - $x(x - 4)$ matches $x^2 - 4x$ - $4x(x + 1)$ matches $4x^2 + 4x$ - $-4x^2 - 2x + 5$ remains as is This completes the matching of expressions to their simplified forms or graphs.