In the expansion of (1+x)^4, what is the coefficient of x^3?

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Multiple Choice

In the expansion of (1+x)^4, what is the coefficient of x^3?

Explanation:
Think of expanding by selecting terms from each factor (1+x). The coefficient of x^k in (1+x)^4 comes from choosing x from k of the four factors and 1 from the rest, and there are C(4,k) ways to do that. For the x^3 term, you choose x from three factors and 1 from one, giving C(4,3) = 4 ways. So the x^3 term has coefficient 4. (Expanding fully shows 1 + 4x + 6x^2 + 4x^3 + x^4, confirming the coefficient.)

Think of expanding by selecting terms from each factor (1+x). The coefficient of x^k in (1+x)^4 comes from choosing x from k of the four factors and 1 from the rest, and there are C(4,k) ways to do that. For the x^3 term, you choose x from three factors and 1 from one, giving C(4,3) = 4 ways. So the x^3 term has coefficient 4. (Expanding fully shows 1 + 4x + 6x^2 + 4x^3 + x^4, confirming the coefficient.)

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