To find the coefficient of the term x9 y in the binomial expansion of (2y + 4x)4, we can first set up the expression as per the binomial theorem, which states that:
(a + b)n = ∑_{k=0}^{n} {n \choose k} a^{n-k} b^{k}
In our case, a = 2y, b = 4x, and n = 4. Now, the term of interest will be represented as:
{n \choose k} (2y)^{4-k} (4x)^{k}
We need to determine the values of k such that the resultant term contains x9 and y. The exponent of x can be derived from (4x)^k, which gives an exponent of k. Therefore, for our targeted term x9, we need:
k = 9
However, since we are expanding (2y + 4x)4, and k can only take values from 0 to 4, there will be no possible term where we will end up with x9 in the expansion.
Consequently, we conclude that the coefficient of the term x9 y in the expansion of (2y + 4x)4 is 0.