Expand (a+1 a )^ 4 - Vidyadip

Question

Expand $\left(\sqrt{a}+\frac{1}{\sqrt{a}}\right)^{4}$

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Answer

$ \begin{aligned} &\left(\sqrt{a}+\frac{1}{\sqrt{a}}\right)^{4} \\ &={ }^{4} \mathrm{C}_{0}(\sqrt{a})^{4}\left(\frac{1}{\sqrt{a}}\right)^{0}+{ }^{4} \mathrm{C}_{1}(\sqrt{a})^{3}\left(\frac{1}{\sqrt{a}}\right)^{1}+{ }^{4} \mathrm{C}_{2}(\sqrt{a})^{2}\left(\frac{1}{\sqrt{a}}\right)^{2} \\ &+{ }^{4} \mathrm{C}_{3}(\sqrt{a})^{1}\left(\frac{1}{\sqrt{a}}\right)^{3}+{ }^{4} \mathrm{C}_{4}(\sqrt{a})^{0}\left(\frac{1}{\sqrt{a}}\right)^{4} \\ &=a^{2}+4(\sqrt{a})^{2}+6+4 \frac{1}{(\sqrt{a})^{2}}+\frac{1}{a^{2}} \\ &=a^{2}+4 a+6+\frac{4}{a}+\frac{1}{a^{2}} \end{aligned} $

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