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Coefficient of X^2 Y^2 in expansion of (x+y)^4

User Jeewan
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1 Answer

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Gievn the expression

(x+y)^4

We will expand this using binomial expansion:

Note that in binomial expansion, as the power of x is decreasing, that of y will be decreasing

(x+y)^4 = x^4y^0 + x^3y^1 + x^2y^2 + x^1y^3 + x^0y^4

(x+y)^4 = x^4 + x^3y + x^2y^2 + xy^3 + y^4

Next is input the coefficient according to pascal triangle. Since the degree of the expression is 4, the coefficient for each term will be 1, 4, 6, 4, 1

Fix in the coefficient:

(x+y)^4 = 1x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + 1y^4

(x+y)^4 = x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4

From the expansion, the coefficient of x^2y^2 is 6

User Shubham Mittal
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