Answer: nCr aⁿ⁻ʳ bʳ.
- A nCr aⁿ bʳ
- B nPr aⁿ⁻ʳ bʳ
- C nCr aʳ bⁿ
- D nCr aⁿ⁻ʳ bʳ
Correct answer: D. nCr aⁿ⁻ʳ bʳ
Explanation: General term T(r+1) = nCr x a<sup>n-r</sup> x b<sup>r</sup>, for r = 0, 1, 2, ..., n.
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