If the term independent of x in the expansion of ( + 2x^3 - x^6 ) (x - 1 x^2 )^9 is 42 , then the value of is

Step-by-step solution

The general term in the expansion of (x - 1 x^2 )^9 is T_ r+1 = ⁹C_ r (x)^ 9-r (- 1 x^2 )^r = ⁹C_ r (-1)^r x^ 9-3r The term independent of x in ( + 2x^3 - x^6 ) (x - 1 x^2 )^9 is the sum of: (coefficient of x^0 in the binomial expansion) + 2 (coefficient of x⁻³ in the binomial expansion) - 1 (coefficient of x⁻⁶ in the binomial expansion) For x^0 , 9 - 3r = 0 r = 3 . The coefficient is ⁹C₃ (-1)^3 = -84 . For x⁻³ , 9 - 3r = -3 r = 4 . The coefficient is ⁹C₄ (-1)^4 = 126 . For x⁻⁶ , 9 - 3r = -6 r = 5 . The coefficient