Answer: (2n)C4.
- A (2n)C4
- B nC4 + nC2 + nC0
- C nC2 × nC2
- D (nC4)²
Correct answer: A. (2n)C4
Explanation: Combine bases: (1+x)ⁿ·(1+x)ⁿ=(1+x)2n. General term: T(r+1)=C(2n,r)xʳ. For the x⁴ term set r=4: coefficient is C(2n,4)=(2n)C4. Convolution of individual terms is equivalent but the merged form gives this directly.
Row n of Pascal's triangle gives the coefficients nC0, nC1, ..., nCn for the expansion of (a+b)ⁿ; each number is the sum of the two numbers diagonally above it, a direct visual proof of the identity nCr = (n-1)C(r-1) + (n-1)Cr.
Concept context
Expansion of (a+b) n , general term, middle term, binomial coefficients, and greatest term