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AP EAMCET202316 May 2023Evening ShiftMathematicsBinomial TheoremActual

Thecoefficientof x^3 in the expansion of (1-2 x)^ 1 2 (1+3 x)^ 1 3 is

Options

  1. A- 20 3
  2. B20 3
  3. C17 3
  4. D- 17 3

Correct answer

A. - 20 3

Step-by-step solution

(1-2 x)^ 1 / 2 (1+3 x)^ -1 / 3 = (1+ 1 2 (-2 x)+ 1 2 ( 1 2 -1 ) 2-1 (-2 x)^2+ 1 2 ( 1 2 -1 ) ( 1 2 -2 ) 3.2 .1 (-2 x)^3+ ) aligned & [1- 1 3 (3 x)+ (- 1 3 ) (- 1 3 -1 ) 2.1 (3 x)^2+ . & . (- 1 3 ) (- 1 3 -1 ) (- 1 3 -2 ) 3.2 .1 (3 x)^3+ ] aligned Coefficient of x^3 . aligned & = 1 6 (- 1 3 ) (- 4 3 ) (- 7 3 ) 27- 1 2 (- 1 3 ) (- 4 3 ) 9 & + 1 6 1 2 (- 1 2 ) (- 3 2 )(-8)- 1 2 1 2 (- 1 2 ) 4=- 20 3 aligned

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