Question

Coefficient of $x^{13}$ in the expansion of $(1-x{)}^5{\left(1+x+x^2+x^3\right)}^4$ is

• A. 4
• B. 6
• C. 32
• D. 5

Answer 1

Answer: (A)

Expression $=(1-x{)}^5\cdot (1+x{)}^4{\left(1+x^2\right)}^4$
$=(1-x){\left(1-x^2\right)}^4{\left(1+x^2\right)}^4$
$=(1-x){\left(1-x^4\right)}^4$
$\therefore$ Coefficient of $x^{13}=-{}^4{C}_3(-1{)}^3=4$