hi

begin with some substitution as hinted by the question

1+14(x+kx^2)+91(x+kx^2)^2+364(x+kx^2)^3+91(x^2+2kx ^3+k^2x^4)+364(x^3+3kx^4+3x(kx^2)^2+(kx^2)^3)

Given that the coefficient of is 0 , so we need to know the coefficient of x^3 only . To expand the whole thing would be tedious , so we expand those parts where is .

coefficient of x^3 :