Question

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

Answer 1

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

$\Rightarrow [{{}^{5}C}_0+{{}^{5}C}_1{x}^2+{{}^{5}C}_2{x}^4....][{{}^{4}C}_0+{{}^{4}C}_{1}x+{{}^{4}C}_2{x}^2....]$

$\Rightarrow {{}^{5}C}_1{{}^{4}C}_3{x}^5+{{}^{5}C}_2{{}^{4}C}_1{x}^5$

$\Rightarrow [5\times 4+10\times 4]x^5$

$\Rightarrow [20+40]x^5$

$\Rightarrow 60x^5$

Hence, the answer is $60x^5.$