Multinomial Theorem Proof. Proceed by induction on m. Proving the multinomial theorem by induction.
In addition we shall use multi index notation. This is called the multinomial formula. Look it up.
For the induction step suppose the multinomial theorem holds for m.
Proceed by induction on m. Assume that and that the result is true for when treating as a single term and using the induction hypothesis. As a proof by induction use something like x 1 x 2 dots x n x n 1 r y x n 1 r say with y x 1 x 2 dots x n. Since this can be rewritten as.
