1. **State the problem:** Simplify the expression $$(a-2)^2 \times (a+2)^2$$. 2. **Recall the formula:** The expression is a product of two squares. We can use the property $$(x^2)(y^2) = (xy)^2$$ to combine them. 3. **Apply the property:** $$ (a-2)^2 \times (a+2)^2 = \big((a-2)(a+2)\big)^2 $$ 4. **Simplify inside the parentheses:** $$(a-2)(a+2) = a^2 - 2^2 = a^2 - 4$$ 5. **Substitute back:** $$ \big(a^2 - 4\big)^2 $$ 6. **Expand the square:** $$ (a^2 - 4)^2 = (a^2)^2 - 2 \times a^2 \times 4 + 4^2 = a^4 - 8a^2 + 16 $$ **Final answer:** $$ a^4 - 8a^2 + 16 $$