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)`


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