Question

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

• A. $30$
• B. $60$
• C. $40$
• D. $Noneofthese$

Answer 1

The correct option is B $60$

As we know that, the general term of the expansion ${(a+b)}^n$ is given as-

$T_{r+1}={}^n{C}_r{a}^r{b}^{n-r}$

Therefore,

${(1+x^2)}^5{(1+x)}^4$

$=({}^5{C}_0+{}^5{C}_1{x}^2+{}^5{C}_2{x}^4+.....+{}^5{C}_5{x}^{10})({}^4{C}_0+{}^4{C}_{1}x+{}^4{C}_2{x}^2+.....+{}^4{C}_4{x}^4)$

Therefore,

Coefficient of $x^5={}^5{C}_1\cdot {}^{4}C3+{}^5{C}_2\cdot {}^4{C}_1=5\times 4+10\times 4=20+40=60$