`(1/x + 2y)^6` Use the Binomial Theorem to expand and simplify the expression.

A simple method used to solve this binomial is the use of pascal's triangle: 

The expansion of our example is expanded as follows using pascal's triangle: 

Now let's  use the above expansion to solve our problem:

`(1/x + 2y)^6 = 1 *(1/x)^6 + 6 * (1/x)^5 * (2y) + 15 * (1/x)^4 * (2y)^2 + 20 * (1/x)^3 * (2y)^3 + 15 * (1/x)^2 * (2y)^4 + 6 * (1/x) * (2y)^5 + 1*(2y)^6`

Now we can evaluate the above expression: 

`(1/x + 2y)^6 = (1/x)^6 + 12 *(1/x)^5 * y + 15 * 4 * (1/x)^4 * y^2 + 20 * 8 * (1/x)^3 *y^3 + 15 * 16 * (1/x)^2 * y^4 + 6 * 32 * (1/x) * y^5 + 64 * y^6`

We can simply the answer as follows:

`(1/x + 2y)^6 = 64*y^6 + (192*y^5)/x + (240*y^4)/(x^2) + (160*y^3)/(x^3) + (60*y^2)/(x^4) + (12*y)/(x^5) + 1/(x^6)`

This is the final answer