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AP EAMCET202422 May 2024Morning ShiftMathematicsBinomial TheoremActual

|x| 1 , the coefficients of x^2 in the power series expansion of x^4 (x+1)(x-2) is

Options

  1. A3
  2. B0
  3. C-1
  4. D-3

Correct answer

B. 0

Step-by-step solution

aligned & x^4 (x+1)(x-2) = x^4 3 [ 1 (x-2) - 1 (x+1) ] & = x^4 3 [ -1 2 (1-x)⁻¹-(1+x)⁻¹ ] aligned aligned & = x^4 3 [ -1 2 - x 2 - x^2 2 - x^3 2 + -1+x-x^2+x^3- ] & =- x^4 6 - x^5 6 - x^6 6 - x^7 6 + - x^4 3 + x^5 3 + aligned So, coefficient of x^2=0 .

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