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Manipal MET2015MathematicsBinomial Theorem

The term independent of x in the expansion of (x- 1 x )^4 (x+ 1 x )^3 , is

Options

  1. A-3
  2. B0
  3. C1
  4. D3

Correct answer

B. 0

Step-by-step solution

We have, gathered (x- 1 x )^4 (x+ 1 x )^3 = ( ^4 C₀ x^4- ^4 C₁ x ^2+ ^4 C₂- ^4 C₃ 1 x^2 + ^4 C₄ 1 x^4 ) ( ^3 C₀ x^3+ ^3 C₁ x+ ^3 C₂ 1 x + ^3 C₃ 1 x^3 ) gathered Clearly, there is no term free from x on RHS. Therefore, the term independent of x on LHS is zero.

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