Answer: a² + 2ab + b².
- A a² + b²
- B a² + ab + b²
- C a² + 2ab + b²
- D a² - 2ab + b²
Correct answer: C. a² + 2ab + b²
Explanation: (a+b)<sup>2</sup> = a<sup>2</sup> + 2ab + b<sup>2.</sup> Using binomial theorem: 2C0 a<sup>2</sup> + 2C1 ab + 2C2 b<sup>2.</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