**This is a question that was recently asked on Quora**:

it’s easy to expand

or

or some other but what about aka.

**Here’s my answe**r:

Just have Wolfram|Alpha do it for you :-).

But if you were on a desert island without access to Wolfram Alpha, here’s how you might think it through:

Are you already comfortable with the Binomial Theorem? Here it is again, but stated in a particular way that I think we’ll like.

Look at it and make sure you understand it, and verify that it really is equivalent to the formulation of the Binomial Theorem you know.

**Now, for the big trick. It turns out the above statement holds true not for just but for all real . The only catch is that this often results in an infinite series. **(These series results can also be obtained by Taylor expansion.)

In particular, it works for :

Now, rewriting your original expression as gives

which is the same result Wolfram Alpha will spit back.

Hope that helps!

### Like this:

Like Loading...

*Related*