Answer: 45.
- A 10
- B 10C4
- C 45
- D 120
Correct answer: C. 45
Explanation: T(r+1) = 10Cr x<sup>10-r</sup> x x<sup>-2r</sup> = 10Cr x<sup>10-3r</sup>. For x<sup>4</sup>: 10-3r=4, r=2, coefficient = 10C2 = 45.
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