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KCET2007MathematicsBinomial Theorem

The ninth term of the expansion (3 x- 1 2 x )⁸ is

Options

  1. A1 512 x⁹
  2. B-1 512 x⁹
  3. C-1 256 x⁸
  4. D1 256 x⁸

Correct answer

D. 1 256 x⁸

Step-by-step solution

The general term of the expansion (x+a)^ n is T_ r+1 = n r x^ n-r a^ r . We have, (3 x- 1 2 x )⁸ . Here, r=8, x=3 x, a= (- 1 2 x ), n=8 Nineth term, T₉= 8 8 (3 x)⁸⁻⁸ ( -1 2 x )⁸ = 1 256 x⁸

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