Let a=((1+2x+3x2)6+(1−4x2)6) ∴ Coefficient of x2 in the expansion of the product (2−x2)((1+2x+3x2)6+(1−4x2)6) =2( Coefficient of x2 in a )−1 (Constant of expansion) In the expansion of ((1+2x+3x2)6+(1−4x2)6). Constant =1+1=2 Coefficient of x2=[ Coefficient of x2 in (6C0(1+2x)6(3x2)0)] +[ Cofficient of x2 in (6C1(1+2x)5(3x2)1)]−[6C1(4x2)] =60+6×3−24=54 ∴ The coefficient of x2 in (2−x2)((1+2x+3x2)6+(1−4x2)6) =2×54−1(2)=108−2=106