Answer: 58√2.
- A 82√2
- B 82
- C 58
- D 58√2
Correct answer: D. 58√2
Explanation: Using (a+b)5 + (a-b)5 = 2[5C0 a5 + 5C2 a3 b2 + 5C4 a b4]. With a=sqrt(2), b=1: 2[4sqrt(2)+10*2sqrt(2)+5sqrt(2)] = 2[4+20+5]sqrt(2) = 58sqrt(2).
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