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AP EAMCET2016MathematicsQuadratic Equation

The coefficient of x^4 in the expansion of (1-x+x^2-x^3 )^4 is

Options

  1. A31
  2. B30
  3. C25
  4. D-14

Correct answer

A. 31

Step-by-step solution

In the expansion (1-x+x^2-x^3 )^4 aligned & = (1+x^2-x-x^3 )^4= [ (1+x^2 )-x (1+x^2 )^4 ] & = [ (1+x^2 )(1-x)^4 ]= (1+x^2 )^4(1-x)^4 & = (1+4 x^2+1+6 x^4+4 x^6+x^8 ) & (1-4 x^2+6 x^2-4 x^3+x^4 ) & Coefficient of x^4=1+4 6+6 & =1+24+6=31 aligned

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