What is x4-81 factored?

What we need here:

"The difference of two squares is the same as (their sum) times (their difference)."

x^4 is the square of x² .
81 is the square of 9 .
Their difference is the same as (x² + 9) times (x² - 9).

But (x² - 9) is also the difference of two squares,
so it's the same thing as (x+ 3) times (x-3).

So the complete factored form of the original expression is

(x^4 - 81) = (x² + 9) (x+3) (x - 3)