Math, asked by mateen2268, 10 months ago

Coefficient of x^2y^3z^4 in the expansion of (x+y+z) ^9 is equal to

Answers

Answered by aashishrajput263
4

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Step-by-step explanation:

Answered by NirmalPandya
0

The coefficient of the term x^2y^3z^4 in the expansion of (x+y+z) ^9 is 1260.

Given,

An expression: (x+y+z) ^9 .

To Find,

The coefficient of the term x^2y^3z^4.

Solution,

The method of finding the coefficient of the term x^2y^3z^4 in the expansion of (x+y+z) ^9  is as follows -

We know by the multi-binominal theorem that the coefficient of the term x^py^mz^l in the expansion of (ax+by+cz)^{n} is \frac{n!*a^pb^mc^l}{p! \ m! \ l!}.

Here in this problem, p = 2, m = 3, l = 4, n = 9, a = b = c = 1.

So putting all the values in the formula, the coefficient will be \frac{9!*1^21^31^4}{2! \ 3! \ 4!} = \frac{1*2*3*4*5*6*7*8*9}{2*6*24}

=1260

Hence, the coefficient of the term x^2y^3z^4 in the expansion of (x+y+z) ^9 is 1260.

#SPJ3

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