Question

The coefficient of $x^4$ in the expansion of $\left(1-x^2+x^3-x^4\right){\left(1-2x^2\right)}^6$ is co-prime with

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (A), (B), (C), (D)

$T_{r+1}$ in ${\left(1-2x^2\right)}^6$
${}^6{C}_r(-2{)}^r\cdot x^{2r}$
$\therefore$ Coefficient of $x^4$ in $\left(1-x^2+x^3-x^4\right){\left(1-2x^2\right)}^6=1\times {}^6{C}_2(-2{)}^2-{}^6{C}_1(-2)-{}^6{C}_0=71$.