Question

Expand the following:

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

Answer 1

Given expression: `(2x + 1/x)^3`

Step-wise calculation using the binomial expansion formula for (a + b)³:

(a + b)³ = a³ + 3a²b + 3ab² + b³

Here, `a = 2x` and `b = 1/x`.

Now, expand:

1. a³ = (2x)³ = 8x³

2. `3a^2b = 3(2x)^2 xx 1/x`

`3a^2b = 3 xx 4x^2 xx 1/x`

3a²b = 12x

3. `3ab^2 = 3(2x) xx (1/x)^2`

`3ab^2 = 3 xx 2x xx 1/x^2`

`3ab^2 = 6/x`

4. `b^3 = (1/x)^3`

`b^3 = 1/x^3`

Adding all these terms together:

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