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BITSAT2016MathematicsBinomial TheoremActual

If the sum of odd numbered terms and the sum of even numbered terms in the expansion of (x+a)^ n are A and B respectively, then the value of (x²- . .a² )^ n is

Options

  1. AA ²- B ²
  2. BA ²+ B ²
  3. C4 AB
  4. DNone

Correct answer

A. A ²- B ²

Step-by-step solution

array r (x+a)^ n = n 0 x^ n + n 1 x^ n-1 a+ n 2 x^ n-2 a² + n 3 x^ n-3 a³+ n 4 x^ n-4 a⁴+ . = ( n 0 x^ n + n 2 x^ n-2 a²+ n 4 x^ n-4 a⁴+ . )+ + ( n 1 x^ n-1 a+ n 3 x^ n-3 a³+ n 5 x^ n-5 a⁵ )+ . array =A+B ....(i) Similarly, (x-a)^ n =A-B ....(ii) Multiplying eqns. (1) and (2), we get ( x ²- a ² )^ n = A ²- B ²

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