1. **State the problem:** Simplify and expand the expression $(x-2)^2$. 2. **Formula used:** The square of a binomial $(a-b)^2$ is given by $$ (a-b)^2 = a^2 - 2ab + b^2 $$ 3. **Apply the formula:** Here, $a = x$ and $b = 2$, so $$ (x-2)^2 = x^2 - 2 \times x \times 2 + 2^2 $$ 4. **Calculate each term:** $$ x^2 - 4x + 4 $$ 5. **Final answer:** The expanded form of $(x-2)^2$ is $$ x^2 - 4x + 4 $$