Use the Multinomial Theorem to find the coefficient of x^7*y^8 in
(2*x^3 + 3*x^2*y + 5*x*y^2 + 7*y^3)^5.
the coefficient is where the sum is taken over all integer solutions of the system: and note
that the condition is a result of the above equations. also see that we actually have: one
way to find all solutions is to consider four cases it will take less than 5 minutes of your time!