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

1 Answer
Aug 1, 2015

Answer:

#-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)#