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📐 Mathematics  ·  Binomial Theorem  ·  JEE

(a - b)⁴ = a⁴ - 4a³b + 6a²b² ___.

Answer: - 4ab³ + b⁴.

  • A + 4ab³ + b⁴
  • B + 4ab³ - b⁴
  • C - 4ab³ - b⁴
  • D - 4ab³ + b⁴

Correct answer: D. - 4ab³ + b⁴

Explanation: (a-b)<sup>4</sup> = a<sup>4</sup> - 4a<sup>3b</sup> + 6a<sup>2b</sup><sup>2</sup> - 4ab<sup>3</sup> + b<sup>4</sup> (alternating signs).

Pascal's Triangle: Binomial Coefficients11112113311464115101051n=0n=1n=2n=3n=4n=5Each entry = sum of the two entries diagonally above it (Pascal's identity); row n gives nC0...nCn

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

Read the full Binomial Theorem notes →