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Manipal MET2021MathematicsBinomial Theorem

The middle term in the expansion of (x- 1 2 y )¹⁰ is

Options

  1. A-63 x^5 y^5
  2. B- 63 x^5 y^5 8
  3. C63 x^5 y^5
  4. D63 x^5 8 y^5

Correct answer

B. - 63 x^5 y^5 8

Step-by-step solution

Middle term =T₆=T_ 5+1 aligned & = ¹⁰ C₅(x)^5 (- 1 2 y )^5= 10! 5! 5! (x)^5 (-2)^5 y^5 & =- 10 9 8 7 6 5 4 2 3 2^5 x^5 y^5 & =- 63 8 x^5 y^5 aligned

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