Question

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

Answer 1

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

Explanation:

Given `x^8 - 1/81`

Using difference of square `a^2 -b^2 = (a-b)(a+b)`
`=> (x^4)^2 -(1/9)^2`

`=>(x^4 -1/9)(x^4 +1/9)`

Use the difference of square again...

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