In the expansion of (x + y)^4, what is the coefficient of x^2 y^2?

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Multiple Choice

In the expansion of (x + y)^4, what is the coefficient of x^2 y^2?

Explanation:
When expanding (x+y)^4, think about choosing x or y from each of the four factors. To get the term x^2 y^2, you must pick x twice and y twice. The number of ways to do that is the binomial coefficient C(4,2) = 6, which counts how many times this term appears in the expansion. Equivalently, the expansion runs with coefficients 1, 4, 6, 4, 1 for x^4, x^3y, x^2y^2, xy^3, and y^4 respectively; the x^2y^2 term has coefficient 6.

When expanding (x+y)^4, think about choosing x or y from each of the four factors. To get the term x^2 y^2, you must pick x twice and y twice. The number of ways to do that is the binomial coefficient C(4,2) = 6, which counts how many times this term appears in the expansion.

Equivalently, the expansion runs with coefficients 1, 4, 6, 4, 1 for x^4, x^3y, x^2y^2, xy^3, and y^4 respectively; the x^2y^2 term has coefficient 6.

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