Verified Answer :

HomertheGenius

The binomial expansion: \(T_{k+1}= \frac{n!}{(n-k+1 )!}a^{n-k} b^{k}\)
a = 2y,  b = 4 x^3, n = 4
( x )^3k = x^ 9
k = 3
\(T_{4}= \frac{24}{6}(2y) ^{3-1} (4x^{3} )^{3}\)
\(T4=512 x^{9} y\)
Answer: the coefficient is 512.

Answer: The coefficient of the \(x^9y\) term in the binomial expansion is 512.

Step-by-step explanation:

Since we have given that

\((2y+4x^3)^4\)

We have to find the coefficient of \(x^9y\) term in the binomial expansion.

\(T_2=^4C_1(2y)^1(4x^3)^3\\\\T_2=4\times 2\times 4^3x^9y\\\\T_2=512x^9y\)

Hence, the coefficient of the \(x^9y\) term in the binomial expansion is 512.

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