Question

Expand the following:

`(2a+1/a)^3`

Answer 1

Using the identity

(a + b)³ = a³ + 3a²b + 3ab² + b³

Here, let a = 2a, b = `1/a`

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

= `8a^3 + 3xx4a^2xx1/a + 6axx1/a^2 + 1/a^3`

= `8a^3 + 12a^2xx1/a + 6/a + 1/a^3`

∴ `(2a + 1/a)^3 = 8a^3 + 12a + 6/a + 1/a^3`