Question

How do you factor `-1/81 + x^8`?

Answer 1

`-1/81+x^8 = (x^4+1/9)(x^2+1/3)(x^2-1/3)`

Explanation:

`-1/81+x^8`
`color(white)("XXXX")` `=(x^4)^2-(1/9)^2`

and since this is the difference of squares:
`color(white)("XXXX")`#=(x^4+1/9)(x^4-1/9)

which can be written:
`color(white)("XXXX")` `(x^4+1/9)((x^2)^2-(1/3)^2)`

with another difference of squares:
`color(white)("XXXX")` `=(x^4+1/9)(x^2+1/3)(x^2-1/3)`