(a²-1)(a³-1)

To simplify the expression \((a^2 - 1)(a^3 - 1)\), we can use the factorizations of \(a^2 - 1\) and \(a^3 - 1\).

1. Factor \(a^2 - 1\): \[ a^2 - 1 = (a - 1)(a + 1) \]

2. Factor \(a^3 - 1\): \[ a^3 - 1 = (a - 1)(a^2 + a + 1) \]

Now, we can substitute these factorizations back into the original expression:

\[ (a^2 - 1)(a^3 - 1) = (a - 1)(a + 1)(a - 1)(a^2 + a + 1) \]

Next, we can combine the common factors:

\[ = (a - 1)^2(a + 1)(a^2 + a + 1) \]

Thus, the simplified expression is:

\[ \boxed{(a - 1)^2(a + 1)(a^2 + a + 1)} \]