Coefficient of x10 in the expansion of 1+x210x2+2+1x25 is

Coefficient of x10 in the expansion of 1+x210x2+2+1×25 is

Coefficient of $x^{10}$ in the expansion of ${(1 + x^{2})}^{10} {(x^{2} + 2 + \frac{1}{x^{2}})}^{5}$ is

${(1 + x^{2})}^{10} (x^{2} + 2 + \frac{1}{x^{2}})$

$= {(1 + x^{2})}^{10} {(x + \frac{1}{x})}^{5} = \frac{1}{x^{5}} {(1 + x^{2})}^{15}$

$∴$ coefficient of $x^{10}$ in $(1 + x^{2}) {(x^{2} + 2 + \frac{1}{x^{2}})}^{5}$

= coefficient of $x^{15}$ in ${(1 + x^{2})}^{15} = 0 .$