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

The coefficient of x^3y^4 in (3x+2y)^7 is - id34327863333, LuxTheGirl3070

nicolascorrea0207

12.03.2022

The coefficient is 15120.

Step-by-step explanation:

Since, by the binomial expansion formula,

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

Where, $^nC_r=\frac{n!}{r!(n-r)!}$

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.

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