Question

reduce the rational expression to lowest terms:

81a^4 - 1 / 3a - 1

Answer 1

You should try to factor the top and factor the bottom.

81a^4 - 1 is the difference of 2 squares

(9a^2)^2 - (1)^2 = (9a^2 + 1)(9a^2 - 1) however,
the (9a^2 - 1) is also the difference of 2 squares so the top factors into
(9a^2 + 1)(3a + 1)(3a - 1) all over (3a-1)

The 3a - 1 's cancel and you are left with
(9a^2 + 1)(3a + 1) as the answer... Depending upon what they want you could foil this back out and get
27a^3 + 9a^2 + 3a + 1