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AP EAMCET201824 Apr 2018Morning ShiftMathematicsBinomial TheoremActual

The coefficient of x^4 in the power series expansion of x^2-1 (x^2+1 ) (x^2+2 ) is

Options

  1. A15 16
  2. B15 4
  3. C- 13 8
  4. D77 324

Correct answer

C. - 13 8

Step-by-step solution

Using binomial expansions, aligned & (x^2-1 ) (x^2+1 ) (x^2+2 ) = 1 2 (x^2-1 ) (1+x^2 )⁻¹ (1+ x^2 2 )⁻¹ = & 1 2 [ (x^2-1 ) (1-x^2+x^4 ) (1- x^2 2 + x^4 4 ) ] = & 1 2 [ (x^2-1 ) (1- x^2 2 + x^4 4 -x^2+ x^4 2 +x^4 ) ] = & 1 2 [ (x^2-1 ) (1- 3 2 x^2+ 7 4 x^4 ) ] = & 1 2 [-1+ 3 2 x^2- 7 4 x^4+x^2- 3 2 x^4 ] aligned taking coefficient of x^4 , = 1 2 (- 7 4 - 3 2 )= 1 2 ( -13 4 )= -13 8 .

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