Question

What is the coefficient of the x9y-term in the binomial expansion of (2y + 4x3)4? 4 32 128 512

Answer 1

512 is the coefficient of the x9y-term                             

Answer 2

Answer:- 512

Explanation:-

We know that
`(m+1)^(th),\ (T_(m+1))` in the binomial expansion
`(p+q)^n` is given by

`T_(m+1)=^nC_m\ p^(n-m)q^m`

Assume that
`x^9y` occurs in the
`(m+1)^(th)` term of the expansion of
`(2y+4x^3)^4=(4x^3+2y)^4`

`T_(m+1)=^4C_m\ (4x^3)^(4-m)(2y)^m`

Comparing power of x and y in
`x^9y` we get m=1

Thus term for m=1
`=\ ^4C_1\ (4x^3)^(3)(2y)^1=^4C_1=(4!)/((4-1)!1!)(64x^9)(2y)=4(128x^9y)=512x^9y`

Thus the coefficient of
`x^9y` is 512.