Question

Factorise the following:

`a^4 - 1/81`

Answer 1

To factorise `a^4 - 1/81`, we can treat it as a difference of squares.

First, rewrite the expression:

`a^4 - 1/81 = (a^2)^2 - (1/9)^2`

Now, apply the difference of squares formula:

A² – B² = (A – B) (A + B)

In this case, A = a² and `B = 1/9`.

So, we get:

`(a^2 - 1/9) = (9 - 1/3) (a + 1/3)`

Thus, the factorised form of `a^4 - 1/81 = (a - 1/3) (a + 1/3) (a^2 + 1/9)`