I'm trying to proof that the following language is not a regular language using the pumping lemma:

$L= \{a^nb^m2^{n\*m} \mid m,n \ge 0 \} $

I tried to build the string by assuming that m,n are the same number p, $w = 0^p1^p2^{p^2}$.
but I'm stuck with what should I do next?

I know how to solve for example the problem $L= \{0^n1^n \mid n \ge 0 \} $.
I read many times the theorem:

> 
> If $L$ is regular, we are able to divide $w$ up into three parts
> $s=xyz$ where:
> 
> 
> $|xy|\leq p$,
> 
> 
> $|y| > 0$,
> 
> 
> $xyz \in L \Leftrightarrow xy^{i}z\in L $ for all $i\in\mathbb{N}$
> 
> 
> 

I would be very grateful if somebody will help me