Answer: 1 + 3x + 3x² + x³.
- A 1 + 3x + 3x² + x³
- B 1 + 3x + x² + x³
- C 1 + x + x² + x³
- D 1 + 3x² + 3x + 1
Correct answer: A. 1 + 3x + 3x² + x³
Explanation: (1+x)<sup>3</sup> = 3C0 + 3C1 x + 3C2 x<sup>2</sup> + 3C3 x<sup>3</sup> = 1 + 3x + 3x<sup>2</sup> + x<sup>3.</sup>
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