Expanding the given expression:

(а-2)(а+2)(а²-2а+4)(a²+2a+4)

First, we expand (a-2)(a+2):
(a-2)(a+2) = a(a) + a(2) - 2(a) - 2(2)
= a² + 2a - 2a - 4
= a² - 4

Next, we expand (a²-2a+4)(a²+2a+4):
(a²-2a+4)(a²+2a+4) = a^4 + 2a^3 + 4a^2 - 2a^3 - 4a^2 - 8a + 4a^2 + 8a + 16
= a⁴ + 2a² + 16

Therefore, the expanded expression is:
(a² - 4)(a⁴ + 2a² + 16)
= a⁶ + 2a⁴ + 16a² - 4a⁴ - 8a² - 64
= a⁶ - 2a⁴ + 8a² - 64