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### 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)