Factor the number 16 and write it as a product of its prime factors:

`16 = 2 * 2 * 2 * 2`

`16 = 2^4`

So write `2^4` in place of `16`,

`x^4 - 2^4`

Rewrite `x^4` as `(x^2)^2` and `2^4` as `(2^2)^2`

`(x^2)^2 - (2^2)^2`

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

`(x^2 + 2^2)(x^2 - 2^2)`

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

`(x^2 + 2^2)(x + 2)(x - 2)`

Simplify by writing `2^2` as `4`,

`(x^2 + 4)(x + 2)(x - 2)`

Thus you have completely factored `x^4 - 16` into `(x^2 + 4)(x + 2)(x - 2)`

`16 = 2 * 2 * 2 * 2`

`16 = 2^4`

So write `2^4` in place of `16`,

`x^4 - 2^4`

Rewrite `x^4` as `(x^2)^2` and `2^4` as `(2^2)^2`

`(x^2)^2 - (2^2)^2`

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

`(x^2 + 2^2)(x^2 - 2^2)`

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

`(x^2 + 2^2)(x + 2)(x - 2)`

Simplify by writing `2^2` as `4`,

`(x^2 + 4)(x + 2)(x - 2)`

Thus you have completely factored `x^4 - 16` into `(x^2 + 4)(x + 2)(x - 2)`

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