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 :

• A. 107
• B. 106
• C. 108
• D. 155

Answer 1

Answer: (B)

coefficient of $ x^2=2 $ coefficient of $x^2 \text { in } $
$ \left(\left(1+2 x+3 x^2\right)^6+\left(1-4 x^2\right) 6\right) $ - constant term
$ \left(1+2 x+3 x^2\right) 6 \displaystyle\sum_{r=0}^6 $
$ { }^6 C_r\left(2 x+3 x^2\right)^r $
$ ={ }^6 C_0+{ }^6 C_1\left(2 x+3 x^2\right)+{ }^6 C_2\left(2 x+3 x^2\right)^2+\ldots $
coefficient of $ x^2=2(18+60-24)-2 $
$ =108-2=106$