Hey geniusgarvil.

If you perform a trinomial expansion on your 2u+4x+4x, you will be able to get a term in regards to u^2*v^3*x^5 if you raise it to the power of (2+3+5) = 10.

If you assume that the highest term contains all the information, then you can verify for yourself by setting one value to the highest and setting the rest equal to zero what the highest value of this term will be, by looking at the relevant coffecient that corresponds to that trinomial term.

So for a term of u^2*v^3*x^5, this will have a trinomial term in the same that a binomial has an nCr term before x^r*y(n-r) and this term is called the multinomial coeffecient:

Multinomial theorem - Wikipedia, the free encyclopedia