Question

Expand the following:

`(3a-1/a)^3`

Answer 1

Using the identity

(a − b)³ = a³ − 3ab(a − b) − b³

Here, let a = 3a, b = `1/a`

`(3a - 1/a)^3 = (3a)^3 - 3(3a) (1/a) (3a - 1/a) - (1/a)^3`

`=27a^3 - 9a(1/a) (3a - 1/a) - 1/a^3`

`=27a^3 - 9(3a - 1/a) - 1/a^3`

`=27a^3 - (27a - 9/a) - 1/a^3`

∴ `(3a - 1/a)^3 = 27a^3 - 27a + 9/a - 1/a^3`