In the expansion of (x + y)^3, what is the coefficient of x y^2?

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Multiple Choice

In the expansion of (x + y)^3, what is the coefficient of x y^2?

Explanation:
In the binomial expansion, the coefficient of a term x^r y^(n−r) comes from the number of ways to pick which factors contribute x and which contribute y. For (x+y)^3, to get x^1 y^2 you need one x and two y’s from the three factors. There are 3 ways to choose which factor provides x, so the coefficient is 3. The term is 3 x y^2, matching the expansion x^3 + 3 x^2 y + 3 x y^2 + y^3.

In the binomial expansion, the coefficient of a term x^r y^(n−r) comes from the number of ways to pick which factors contribute x and which contribute y. For (x+y)^3, to get x^1 y^2 you need one x and two y’s from the three factors. There are 3 ways to choose which factor provides x, so the coefficient is 3. The term is 3 x y^2, matching the expansion x^3 + 3 x^2 y + 3 x y^2 + y^3.

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