Hi! Can someone give me a derivation of the binomial theorem for dummies please, thanks! I'm looking for something intuitive and insightful because I just can't follow my textbook!
(reminder: the theorem is an expansion for (x+y)^n )
Take a simple example: .
To expand that product we take either x or y from each of the six factors.
In order to get we must take an x from each factor. That can be done in only one way.
But to get a term containing , we choose four x’s and two y’s.
We could do it as xxyxxy or yxxyxx for example. That can be done is ways.
In general, .
Just think about the number of ways to choose the terms from the n factors.