In Need of Algreba Factoring Help?

Question

I am in need of help on an algrebra factoring problem.
81r^4-256s^4

Answer 1

81r^4 - 256s^4
Treat this like a difference of two squares:
(9r^2)^2 - (16s^2)^2 = (9r^2 - 16s^2)(9r^2 + 16s^2) ........(1)
9r^2 - 16s^2 can also be treated as a differnce of two squares. Equation (1) becomes:
((3r)^2 - (4s)^2)(9r^2 + 16s^2) = (3r - 4s)(3r + 4s)(9r^2 + 16s^2).
So the final answer is:(3r - 4s)(3r + 4s)(9r^2 + 16s^2).

Answer 2

The expression is the difference of perfect fourth powers.

81r^4 - 256s^4 = (9r² - 16s²)(9r² + 16s²)

= (3r - 4s)(3r + 4s)(9r² + 16s²)