x⁸ - 2x⁶ + 2x² - 1 =
= x⁸ - 1 - 2x²(x⁴ - 1)
= (x⁴ - 1)(x⁴ + 1) - 2x²(x⁴ - 1)
= (x² - 1)(x² + 1)(x⁴ + 1) - 2x²(x² - 1)(x² + 1)
= (x - 1)(x + 1)(x² + 1)(x⁴ + 1) - 2x²(x - 1)(x + 1)(x² + 1)
= (x - 1)(x + 1)(x² + 1)[(x⁴ + 1) - 2x²]
= (x - 1)(x + 1)(x² + 1)(x⁴ - 2x² + 1)
= (x - 1)(x + 1)(x² + 1)(x² - 1)²