1. The problem is to verify the substitution into the wave equation and understand the simplification step. 2. The wave equation given is: $$-a^2 \sin(x - at) = a^2 (-\sin(x - at))$$ 3. Here, the left side is $$-a^2 \sin(x - at)$$ and the right side is $$a^2 (-\sin(x - at))$$. 4. Notice that multiplying $$a^2$$ by $$-\sin(x - at)$$ is the same as $$-a^2 \sin(x - at)$$ because multiplication is distributive over addition and subtraction. 5. So, the right side simplifies to: $$a^2 (-\sin(x - at)) = -a^2 \sin(x - at)$$ 6. Therefore, both sides are equal: $$-a^2 \sin(x - at) = -a^2 \sin(x - at)$$ 7. This confirms the substitution is correct and the equation holds true. In simple terms, the negative sign can be factored out and the expression remains the same on both sides, showing the equality.