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AP EAMCET202315 May 2023Evening ShiftMathematicsQuadratic EquationActual

The coefficient of the highest power of x in the expansion of (x+ x^2-1 )^8+ (x- x^2-1 )^8 is

Options

  1. A64
  2. B128
  3. C256
  4. D512

Correct answer

C. 256

Step-by-step solution

aligned & Since (x+ x^2-1 )^8+ (x- x^2-1 )^8 & =2 array r ^8 C₀ x^8+ ^8 C₂ x^6 (x^2-1 )+ ^8 C₄ x^4 (x^2-1 )^2 .+ ^8 C₆ x^2 (x^2-1 )^3+ ^8 C₈ x^0 (x^2-1 )^4 array . aligned So coefficient of highest power of x aligned & =2 ^8 C₀+ ^8 C₂+ ^8 C₄+ ^8 C₆+ ^8 C₈ & =(1+1)^8+(1-1)^8=2^8=256 aligned

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