p^6 contains a term x1^6. None of your other forms do, and neither does the original polynomial. Hence it's coefficient must be 0. Same reasoning with p^4q. It contains an x1^5*x2 term.I don't think I understand. On what basis do you exclude the possibility of a p6 term? You say that when expanding the expression we get aijkƩx1ix2jx3k where aijk is a coefficient (integer) and i+j+k = 6. But that doesn't exclude the possibility of the case where i=6, j=0, k=0?