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### Factor x^4 - 1

Rewrite 1 as 1^4 (one raised to the power of four),

x^4 - 1^4

You can write x^4 as (x^2)^2 and 1^4 as (1^2)^2,

(x^2)^2 - (1^2)^2

Apply the difference of squares formula a^2 - b^2 = (a + b)(a - b),

(x^2 + 1^2)(x^2 - 1^2)

Again apply the difference of squares formula on the second parenthesis above,

(x^2 + 1^2)(x + 1)(x - 1)

Simplify by rewriting 1^2 as 1,

(x^2 + 1)(x + 1)(x - 1)

Thus you have completely factored the expression x^4 - 1 into (x^2 + 1)(x + 1)(x - 1)