Question

The coefficient of $x^5$ in the expansion of $(1+x^2{)}^5(1+x{)}^4$ is

Answer 1

Coefficient of $x^5$ in $(1+x^2{)}^5(1+x{)}^4$
= Coefficient of $x^5$ in ${(}^5{C}_0+{}^5{C}_1{x}^2+{}^5{C}_2{x}^4+{}^5{C}_3{x}^6+\dots \left)\right({}^4{C}_0+{}^4{C}_{1}x+{}^4{C}_2{x}^2+\dots )$
$={}^5{C}_1\cdot {}^4{C}_3+{}^5{C}_2\cdot {}^4{C}_1$
$=20+40$
$=60$