Question

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

Answer 1

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

 

Answer 2

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

Step-by-step explanation:

Since we have given that

$(2y+4x^3)^4$

We have to find the coefficient of $x^9y$ term in the binomial expansion.

$T_2=^4C_1(2y)^1(4x^3)^3\\\\T_2=4\times 2\times 4^3x^9y\\\\T_2=512x^9y$

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