Answer:
(3x^2 - 1)(3x^2 + 1)(9x^4 + 1).
Step-by-step explanation:
Using the identity for the difference of 2 squares;
a^2 - b^2 = (a - b)(a + b)
we put a^2 = 81x^8 and b^2 = 1 giving
a = 9x^4 and b = 1, so:
81x^8 − 1 = (9x^4 - 1)(9x^4 + 1)
Applying the difference of 2 squares to 9x^4 - 1:
= (3x^2 - 1)(3x^2 + 1)(9x^4 + 1).
