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.
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.