Expanding each term:

(a+1)(a-1)(a^2+1) = a^4 + a^3 - a^3 - a + a^2 + a - a - 1 = a^4 + a^2 - 1

(a^2-1)^2 = a^4 - 2a^2 + 1

Now substituting these back into the original expression:

(a^4 + a^2 - 1) - (a^4 - 2a^2 + 1) - 2a^2
= a^4 + a^2 - 1 - a^4 + 2a^2 - 1 - 2a^2
= 2a^2 - 1 - 1
= 2a^2 - 2

Therefore, the simplified expression is 2a^2 - 2.