# Series expansion/algebra problem

1. Apr 26, 2014

### BOAS

Hi,

i'm revising series expansions and my problem has arisen from an example in my text book, but it's not directly related to the series expansion itself. It's more of an algebra question, where they've made a rearrangement I can't follow...

1. The problem statement, all variables and given/known data

If $n$ is a positive integer find the coefficient of $x^{r}$ in the expansion of $(1 + x)(1 - x)^{n}$ as a series of ascending powers of x.

2. Relevant equations

3. The attempt at a solution

The solution starts by stating the following expressions are equivalent.

$(1 + x)(1 - x)^{n} \equiv (1 - x)^{n} + x(1 - x)^{n}$

If I take this statement to be true, I can follow through the rest of the example without a hitch, but I just can't see what they've done here.

BOAS.

2. Apr 26, 2014

### Pranav-Arora

Let $(1-x)^n=a$, then $a(1+x)=a+ax$. Do you see now? :)

3. Apr 26, 2014

Perfectly.

Thank you!