Let a=((1+2x+3x2)6+(1−4x2)6)
∴ Coefficient of x2 in the expansion of the product (2−x)2((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)+ Coefficient of x2 in (6C1(1+2x)53)−6C1(4)
=6C24+6×3−24
=6=+18−24=54
Then, coefficient of x2 in (2−x)2((1+2x+3x2)6+(1−4x2)6)
=2×54−1(2)=108−2=106