Factorize:

x⁴ – 1

We have:

We can also write this as:

=(x²)² - 1²

Using identity: a² - b² = (a – b)(a + b)

=(x² + 1)(x² – 1)

Again,

Using identity: a² - b² = (a – b)(a + b)

=(x² + 1)(x + 1)(x – 1)