Question

In expansion of ${\left(x^2-x-2\right)}^5$, the coefficient of $x^2$ is

• A. -80
• B. 320
• C. 72
• D. 0

Answer 1

Answer: (D)

$(xC-2{)}^5(1+x{)}^5=-(2-x{)}^5(1+x{)}^5$
$=-\left[{}^5{C}_0{2}^5-{}^5{C}_1{2}^{4}x+{}^5{C}_2{2}^3{x}^2+\dots \dots \right]\left[{}^5{C}_0+{}^5{C}_{1}x+{}^5{C}_2{x}^2+\dots \dots \right]$
$\therefore \text{ Coefficient of }{x}^2\text{ is }=-{}^5{C}_0{2}^5\cdot {}^5{C}_2+{}^5{C}_1\cdot 2^4\cdot {}^5{C}_1-{}^5{C}_2{2}^3=0$