Answer: 8C3 × 3⁵ × x³/8.
- A 56 × 3⁵/8
- B 7C3 x 35 x (x/2)3
- C 8C3 × 3⁵ × x³/8
- D 8C5 × 3⁵ × x³
Correct answer: C. 8C3 × 3⁵ × x³/8
Explanation: T(r+1) = 8Cr x 38-r x (x/2)r. For x3: r=3. T4 = 8C3 x 35 x x3/8 = 56 x 243 x x3/8.
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