Expand:
(x – 1)(x + 1)(x2 + 1)(x4 + 1)
Applying the formula (a + b)(a - b) = a2 - b2 on first two terms
(x – 1)(x + 1)(x2 + 1)(x4 + 1) = (x2 - 1) (x2 + 1)(x4 + 1)
Applying the formula (a + b)(a - b) = a2 - b2 again
⇒ (x – 1)(x + 1)(x2 + 1)(x4 + 1) = (x4 - 1)(x4 + 1)
Applying the formula (a + b)(a - b) = a2 - b2 again
⇒ (x – 1)(x + 1)(x2 + 1)(x4 + 1) = (x8 - 1)
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