How do I factor x^8-80x^4-81

Which two numbers add up to - 80 and multiply to - 81?

-81 and 1

Rewrite the expression using the above

(x^4 - 81) (x^4 + 1)

Rewrite x^4 - 81 in the form; a^2 - b^2, where a = x^2 and b = 9

((x^2) ^2 - 9^2) (x^4 + 1)

Use the Difference of Squares: a^2 - b^2 = (a + b) (a - b)

(x^2 + 9) (x^2 - 9) (x^4 + 1)

Rewrite x^2 - 9 in the form a^2 - b^2, where a = x and b = 3

(x^2 + 9) (x^2 - 3^2) (x^4 + 1)

Use the Difference of Squares; a^2 - b^2 = (a + b) (a - b)

(x^2 + 9 (x + 3) (x - 3) (x^4 + 1)