Answer:
((3 x^2 - 1) (3 x^2 + 1) (9 x^4 + 1))/81
Explanation:
Factor the following:
x^8 - 1/81
Put each term in x^8 - 1/81 over the common denominator 81: x^8 - 1/81 = (81 x^8)/81 - 1/81:
(81 x^8)/81 - 1/81
(81 x^8)/81 - 1/81 = (81 x^8 - 1)/81:
(81 x^8 - 1)/81
81 x^8 - 1 = (9 x^4)^2 - 1^2:
((9 x^4)^2 - 1^2)/81
Factor the difference of two squares. (9 x^4)^2 - 1^2 = (9 x^4 - 1) (9 x^4 + 1):
((9 x^4 - 1) (9 x^4 + 1))/81
9 x^4 - 1 = (3 x^2)^2 - 1^2:
((3 x^2)^2 - 1^2 (9 x^4 + 1))/81
Factor the difference of two squares. (3 x^2)^2 - 1^2 = (3 x^2 - 1) (3 x^2 + 1):
Answer: ((3 x^2 - 1) (3 x^2 + 1) (9 x^4 + 1))/81