Question

Expand the following:

`(5x + 1/x)^2`

Answer 1

Given: `(5x + 1/x)^2`

Step-wise calculation:

1. Use the identity (a + b)² = a² + 2ab + b², where a = 5x and `b = 1/x`.

2. Calculate each term:

a² = (5x)² = 25x²

`2ab = 2 xx 5x xx 1/x`

2ab = 2 × 5

2ab = 10

Since `x xx 1/x = 1`

`b^2 = (1/x)^2`

`b^2 = 1/x^2`

3. Add all terms together:

`(5x + 1/x)^2 = 25x^2 + 10 + 1/x^2`