AP EAMCET2016MathematicsQuadratic Equation
The coefficient of x^4 in the expansion of (1-x+x^2-x^3 )^4 is
Options
- A31
- B30
- C25
- 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