Hello I am in the process of proving that the determinant of the sylvester matrix gives the resultant

f(x) = a_0 x^m + ... + a_{m-1} x + a_m

g(x) = b_0 x^n +... + b_{n-1} x + b_n

(can't get latex to work)

I am supposed to show that the determinant of the Sylvester matrix associated to f,g has degree less than or equal to mn. (see PlanetMath: proof that Sylvester's matrix equals the resultant) I don't understand how it is clear that the degree is less than or equal to mn. I do understand that each a_k or b_k has degree k.

Any help would be appreciated , thank you