...like terms. We get:
$\frac{1}{2}(x-2)^2-\frac{1}{2}(x-4)(x+2) = \frac{1}{2}(x^2-4x+4)-\frac{1}{2}(x^2-2x-8)$
Therefore, the simplified expression is $\frac{1}{2}(x^2-4x+4)-\frac{1}{2}(x^2-2x-8) = 0$.
**Hashtags:**
* #Math
* #algebra
* #problem-solving
* #Math-salad
* #simplifying-expressions