thw coefficient of x²

Question

The coefficient of x^2 in the expansion of the product (2 - x^2)· ((1 + 2x + 3x^2)^6 + (1 - 4x^2)^6) is

Answer 1

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)

=⁶C₂​4+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