Factor completely x^8-1/81

Remember the difference of 2 perfect squares

(a²-b²) = (a-b) (a+b)

1/81 = (1/9) ²

so

x⁸ = (x⁴) ²

x⁸-1/81 = (x⁴) ² - (1/9) ² = (x⁴-1/9) (x⁴+1/9)

oh look, 1/9 = (1/3) ²

x⁴ = (x²) ²

we can factor that first one again

x⁴-1/9 = (x²) ² - (1/3) ² = (x²-1/3) (x²+1/3)

so factored completely is (x²-1/3) (x²+1/3) (x⁴+1/9)

you could go further and force taht first term to be another difference by doing 1/3 = (√ (1/3)) ², but I wouldn't

(x²-1/3) (x²+1/3) (x⁴+1/9) is factored