Question

Expand the following:

`(3x + 1/(3x))^3`

Answer 1

`(3x + 1/(3x))^3`

Using the identity:

(a − b)³ = a³ − 3a²b + 3ab² − b³

Here, let a = 3x, b = `1/(3x)`

`(3x + 1/(3x))^3 = (3x)^3 + 3(3x)^2(1/(3x)) + 3(3x)(1/(3x))^2 + (1/(3x))^3`

= `27x^3 + 3(9x^2) (1/(3x)) + 3(3x) (1/(9x^2)) + 1/(27x^3)`

= `27x^3 + 3((9x^2)/(3x)) + 3((3x)/(9x^2)) + 1/(27x^3)`

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