Factor `x^4 - 81`

This expression can be factored as a difference of two squares, because 81 is a square number and 81 can be written as `3^4`,
`x^4 - 3^4`
Rewrite `x^4` as `(x^2)^2` and `3^4` as `(3^2)^2`,
`(x^2)^2 - (3^2)^2`
Apply the difference of two squares formula `a^2 - b^2 = (a + b)(a - b)`
`(x^2 + 3^2)(x^2 - 3^2)`
Again apply the difference of squares formula,
`(x^2 + 3^2)(x + 3)(x - 3)`
Simplify by writing `3^2` as 9,
`(x^2 + 9)(x + 3)(x - 3)`
Thus we have completely factored the expression `x^4 - 81` into `(x^2 + 9)(x + 3)(x - 3)`

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