Question

Factor completely. x^8-1/81​

Answer 1

Explanation:

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