Question

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

• A. $40$
• B. $50$
• C. $60$
• D. $-50$

Answer 1

The correct option is C $60$

General term of $(1+x^2{)}^5$ is,
$P={}^5{C}_a(x^2{)}^a$
And general term of $(1+x{)}^4$ is,
$Q={}^4{C}_b{x}^b$
So the general term of $(1+x^2{)}^5(1+x{)}^4$ is,
$R={}^5{C}_a(x^2{)}^a\times {}^4{C}_b{x}^b\Rightarrow R={}^5{C}_a{}^4{C}_b{x}^{2a+b}$
The coefficient of $x^5$ will occur when,
$a=1,b=3$ and $a=2,b=1$
The coefficient will be,
$R={}^5{C}_1{}^4{C}_3+{}^5{C}_2{}^4{C}_1=60$