Factor completely 81x8 - 1. (9x4 - 1) (9x4 + 1) (3x2 - 1) (3x2 + 1) (9x4 - 1) (3x2 - 1) (3x2 + 1) (9x4 + 1) (3x2 - 1) (3x2 + 1) (3x2 + 1) (3x2 + 1)

(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).