We have, (1+ax+bx2)(1−2x)18 (1+ax+bx2)(1−‌18C12x+‌18C2(2x2)−‌18C3(2x)3+‌18C4(2x)4.........) Coefficient of x3 is −‌18C3(2)3+a.‌18C2(2)2−b18C1(2) and coefficient of x4 is ‌18C4(2)4−‌18C3(2)3a+‌18C2(2)2b Coefficient of x3 and x4 are zero. ∴−‌18C3(2)3+‌18C2(2)2(a)−‌18C1(2)b=0 ⇒
4×17×16
3×2
−17a+b=0 .........(i) and 80−
32
3
a+b=0 ............(ii) Solving Eqs. (i) and (ii), we get a=16,b=