Answer: The coefficient of the [tex]x^9y[/tex] term in the binomial expansion is 512.
Step-by-step explanation:
Since we have given that
[tex](2y+4x^3)^4[/tex]
We have to find the coefficient of [tex]x^9y[/tex] term in the binomial expansion.
[tex]T_2=^4C_1(2y)^1(4x^3)^3\\\\T_2=4\times 2\times 4^3x^9y\\\\T_2=512x^9y[/tex]
Hence, the coefficient of the [tex]x^9y[/tex] term in the binomial expansion is 512.