The problem asks us to simplify the expression $(a^2+1)(a+1)(a-1)$.

1. Problem Description

The problem asks us to simplify the expression $(a^2+1)(a+1)(a-1)$.

2. Solution Steps

We can first multiply $(a+1)$ and $(a-1)$ using the difference of squares formula.

The difference of squares formula is:

$(x+y)(x-y) = x^2 - y^2$

Using the difference of squares formula with $x=a$ and $y=1$, we have:

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

Now we can substitute this back into the original expression:

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

We can apply the difference of squares formula again with $x=a^2$ and $y=1$:

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

$(a^2)^2 = a^4$

$1^2 = 1$

Therefore,

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

3. Final Answer

$a^4 - 1$