Let . Then, and for some .

Basically you need to argue the followings in order to show that is indeed an ideal of R.

1. Since , it follows immediately that .

Since , we see that . Thus .

2. .

Since and for some , we see that (Use a binomial exapansion ).

3. .

Argue that .

4. or for any .

Argue that or . Since R is a commutative ring (its ideals are two-sided), you need to show either of them.