Question

The term independent of x the expansion of ${\left(\sqrt{x}-\frac{2}{\sqrt{x}}\right)}^{18}$ is

Answer 1

${(\sqrt{x}-\frac{2}{\sqrt{x}})}^{18}$

$T_{\pi +1}{=}^{18}{C}_{\pi }{\left(\sqrt{x}\right)}^{18-\pi }\frac{(-2{)}^{\pi }}{(\sqrt{x}{)}^{\pi }}$

${=}^{18}{C}_{\pi }{(-2)}^{\pi }{x}^{9-\pi }$

$\pi =9$ independent of $x{\to }^{18}{C}_9(-2{)}^9$