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zvonat [6]
3 years ago
7

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

Mathematics
2 answers:
Sonbull [250]3 years ago
4 0
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.

 
Setler [38]3 years ago
4 0

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.

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