Question

Expand (x + 2/x)^5 using binomial theorem?

Answer 1

$$\begin{gathered} {\left(\mathrm{x}+\frac{2}{\mathrm{x}}\right)}^5 \\ ={\mathrm{x}}^5+{}^5\mathrm{C}_1{\mathrm{x}}^4{\left(\frac{2}{\mathrm{x}}\right)}^1+{}^5\mathrm{C}_2{\mathrm{x}}^3{\left(\frac{2}{\mathrm{x}}\right)}^2+{}^5\mathrm{C}_3{\mathrm{x}}^2{\left(\frac{2}{\mathrm{x}}\right)}^3+{}^5\mathrm{C}_4{\mathrm{x}}^1{\left(\frac{2}{\mathrm{x}}\right)}^4+{\left(\frac{2}{\mathrm{x}}\right)}^5 \\ ={\mathrm{x}}^5+\frac{5!}{1!4!}{\mathrm{x}}^4\left(\frac{2}{\mathrm{x}}\right)+\frac{5!}{2!3!}{\mathrm{x}}^3\left(\frac{4}{{\mathrm{x}}^2}\right)+\frac{5!}{2!3!}{\mathrm{x}}^2\left(\frac{8}{{\mathrm{x}}^3}\right)+\frac{5!}{4!1!}{\mathrm{x}}^1\left(\frac{16}{{\mathrm{x}}^4}\right)+\frac{32}{{\mathrm{x}}^5} \\ ={\mathbf{x}}^{\mathbf{5}}\mathbf{+}\mathbf{10}{\mathbf{x}}^{\mathbf{3}}\mathbf{+}\mathbf{40}\mathbf{x}\mathbf{+}\frac{\mathbf{80}}{\mathbf{x}}\mathbf{+}\frac{\mathbf{80}}{{\mathbf{x}}^{\mathbf{3}}}\mathbf{+}\frac{\mathbf{32}}{{\mathbf{x}}^{\mathbf{5}}} \end{gathered}$$