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AP EAMCET2010MathematicsBinomial Theorem

For |x| < 1 5 , the coefficient of x^3 in the expansion of 1 (1-5 x)(1-4 x) is

Options

  1. A369
  2. B370
  3. C371
  4. D372

Correct answer

A. 369

Step-by-step solution

|x| < 1 5 and 1 (1-5 x)(1-4 x) =(1-5 x)⁻¹ (1-4 x)⁻¹ then by binomial expansion = 1+5 x+25 x^2+125 x^3+ 1+4 x+16 x^2+64 x^3+ the coefficient of x^3 in this expansion is =(125+100+80+64)=369

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