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The coefficient of x^3y^4 in (3x+2y)^7 is

2 Answers

5 votes

Answer:

Coefficient of
x^3y^4 in
(3x+2y)^7 is 15120

Explanation:

We know that
(x+y)^(n)) can be expanded in (n+1) terms by using binomial theorem and each term is given as


n_C_(r)x^(n-r)y^(r)

Here value of r is taken from n to 0

we have to determine the coefficient of
x^3y^4 in
(3x+2y)^7

in this problem we have given n=7

We have to determine the coefficient of
x^3y^4

it means in the expansion we have to find the the 3rd power of x and therefore

r=n-3

here n=7

therefore, r=7-3=4

Hence the coefficient of
x^3y^4 can be determine by using formula


n_C_(r)x^(n-r)y^(r)

here n=7, r=4


7_C_(4)x^(7-4)y^(4)

=
(7* 6* 5* 4)/(1* 2* 3* 4) (3x)^3(2y)^4

=
15120x^3y^4

Therefore the coefficient of
x^3y^4 in
(3x+2y)^7 is 15120

User Kelly Johnson
by
8.3k points
5 votes

Answer:

The coefficient is 15120.

Explanation:

Since, by the binomial expansion formula,


(x+y)^n=\sum_(r=0)^n^nC_r x^(n-r) y^r

Where,
^nC_r=(n!)/(r!(n-r)!)

Thus, we can write,


(3x+2y)^7 = \sum_(r=0)^n ^7C_r (3x)^(7-r) (2y)^r

For finding the coefficient of
x^3y^4,

r = 4,

So, the term that contains
x^3y^4 =
^7C_4 (3x)^3 (2y)^4


=35 (27x^3) (16y^4)


=15120 x^3 y^4

Hence, the coefficient of
x^3y^4 is 15120.

User Retronym
by
8.3k points

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