Question

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

• A. $30$
• B. $60$
• C. $40$
• D. None of these

Answer 1

Answer: (B)

${\left(1+x^2\right)}^5\cdot (1+x{)}^4$
$=\left({}^5{C}_0+{}^5{C}_1{x}^2+{}^5{C}_2{x}^4+\dots \right)$
$\left({}^4{C}_0+{}^4{C}_{1}x+{}^4{C}_2{x}^2+{}^4{C}_3{x}^3+{}^4{C}_4{x}^4\right)$
The coefficient of $x^5$ in $\left[{\left(1-x^2\right)}^5(1+x{)}^4\right]$
$={}^5{C}_2\cdot {}^4{C}_1+{}^5{C}_1\cdot {}^4{C}_3$
$=10\cdot 4+4\cdot 5$
$=60$