Answer: 60.
- A 60
- B 61
- C 62
- D 63
Correct answer: A. 60
Explanation: Coeff of x5 in (1+x2)5(1+x)4: from (1+x2)5, only even powers x0, x2, x4 are available (max x10), and from (1+x)4 only powers up to x4 are available. Pairing to total x5: x2 from the first with x3 from the second gives C(5,1)*C(4,3) = 5*4=20; x4 from the first with x1 from the second gives C(5,2)*C(4,1) = 10*4=40. Total = 20+40 = 60.
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