Question

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

Answer 1

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 $=\ ^4C_1\ (4x^3)^{3}(2y)^1=^4C_1=\frac{4!}{(4-1)!1!}(64x^9)(2y)=4(128x^9y)=512x^9y$

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

Answer 2

512 is the coefficient of the x9y-term