Answer: 35.
- A 15
- B 20
- C 30
- D 35
Correct answer: D. 35
Explanation: Write (1+x+x2)5 = ((1+x)(1+x/(1+x)))5... Alternative: coefficient of x4 in (1+x+x2)5. By expansion, coefficient of x4 = 5C4 + 5C3 + 5C2 + 5C1 x coefficient combinations. Standard result using multinomial: equals 35.
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