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

Question

3586 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-12-13T19:49:38

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

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...

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

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