1. The problem is to verify if the equation $4\sqrt{x} + 4\sqrt{y} = 4(\sqrt{x} + \sqrt{y})$ is correct. 2. The distributive property states that $a(b + c) = ab + ac$. 3. Applying the distributive property to the right side: $$4(\sqrt{x} + \sqrt{y}) = 4\sqrt{x} + 4\sqrt{y}$$ 4. The left side is already $4\sqrt{x} + 4\sqrt{y}$. 5. Since both sides are equal, the equation is correct. Final answer: Yes, the equation $4\sqrt{x} + 4\sqrt{y} = 4(\sqrt{x} + \sqrt{y})$ is correct.