Find the cube of: 2 x+1 x - Vidyadip

Question

Find the cube of: $2 x+\frac{1}{x}$

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Answer

$ \left(2 \mathrm{x}+\frac{1}{\mathrm{x}}\right)^3$
$ =(2 \mathrm{x})^3+\left(\frac{1}{\mathrm{x}}\right)^3+3 \times 2 \mathrm{x} \times \frac{1}{\mathrm{x}}\left(2 \mathrm{x}+\frac{1}{\mathrm{x}}\right)$
$ =8 \mathrm{x}^3+\frac{1}{\mathrm{x}^3}+6\left(2 \mathrm{x}+\frac{1}{\mathrm{x}}\right)$
$ =8 \mathrm{x}^3+\frac{1}{\mathrm{x}^3}+12 \mathrm{x}+\frac{6}{\mathrm{x}}$
$ =8 \mathrm{x}^3+12 \mathrm{x}+\frac{6}{\mathrm{x}}+\frac{1}{\mathrm{x}^3}$

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