Respuesta :

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

 

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.