Question

The coefficient of $x^7$ in the expansion of $(1-x-x^3+x^4{)}^8$ is equal to:

• A. $-648$
• B. $792$
• C. $-792$
• D. $648$

Answer 1

Answer: (C)

$-792$

Let $S=(1-x-x^3(1-x){)}^8=((1-x)(1-x^3){)}^8$
$=(1-{{}^{8}C}_1{x}^3+{{}^{8}C}_2{x}^6-....)(1-{{}^{8}C}_1{x}^{}+{{}^{8}C}_2{x}^2-...)$
$\therefore$ Coefficient of $x^7$
$=-{{}^{8}C}_7-{{}^{8}C}_1.{{}^{8}C}_4+{{}^{8}C}_2(-{{}^{8}C}_1)=-792$