Question

What is the coefficient of the x9y-term in the binomial expansion of (2y 4x3)4?

Answer 1

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

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* 2* 4^3x^9y\\\\T_2=512x^9y`

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

Answer 2

The binomial expansion:
`T_(k+1)= (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)= (24)/(6)(2y) ^(3-1) (4x^(3) )^(3)`

`T4=512 x^(9) y`
Answer: the coefficient is 512.