Page "Radical of an ideal" Paragraph 6

Let a and b be in the radical of an ideal I.

Then, for some positive integers m and n, a < sup > n </ sup > and b < sup > m </ sup > are in I.

We will show that a + b is in the radical of I.

Use the binomial theorem to expand ( a + b )< sup > n + m − 1 </ sup > ( with commutativity assumed ):