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)

106

Answer 2

coefficient of $x^2= 2$ coefficient of $x^2$ in $((1 + 2x + 3x^2)^6 + (1 - 4x^2)6)$ - constant term (1 + 2x + 3x^2)6 \sum_\limits{r=0}^6 $^{6}C_{r}\left(2x+3x^{2}\right)^{r}$ $=^{6}C_{0}+^{6}C_{1}\left(2x+3x^{2}\right)+^{6}C_{2} \left(2x+3x^{2}\right)^{2}+ ...$ coefficient of $x^2 = 2(18 + 60 - 24) - 2$ $= 108 - 2 = 106$