Use the binomial theorem to find the coefficient of x^2 in (1 + x)^4.

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

Use the binomial theorem to find the coefficient of x^2 in (1 + x)^4.

Explanation:
The binomial theorem says that (1+x)^4 expands into terms whose coefficients are the binomial coefficients C(4,k) for x^k. To find the coefficient of x^2, take k = 2, so the coefficient is C(4,2) = 6. Therefore, the x^2 term has coefficient 6 (consistent with the expansion 1 + 4x + 6x^2 + 4x^3 + x^4).

The binomial theorem says that (1+x)^4 expands into terms whose coefficients are the binomial coefficients C(4,k) for x^k. To find the coefficient of x^2, take k = 2, so the coefficient is C(4,2) = 6. Therefore, the x^2 term has coefficient 6 (consistent with the expansion 1 + 4x + 6x^2 + 4x^3 + x^4).

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