Question
Find the square of $2 x+\frac{1}{x}+1$
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Answer
$ \left(2 \mathrm{x}+\frac{1}{\mathrm{x}}+1\right)^2$
$=(2 \mathrm{x})^2+\left(\frac{1}{\mathrm{x}}\right)^2+(1)^2+2 \times 2 \mathrm{x} \times \frac{1}{\mathrm{x}}+2 \times \frac{1}{\mathrm{x}} \times 1+2 \times 1 \times 2 \mathrm{x}$
$ =4 \mathrm{x}^2+\frac{1}{\mathrm{x}^2}+1+4+\frac{2}{\mathrm{x}}+4 \mathrm{x}$
$ =4 \mathrm{x}+\frac{1}{\mathrm{x}^2}+5+\frac{2}{\mathrm{x}}+4 \mathrm{x}$
$=(2 \mathrm{x})^2+\left(\frac{1}{\mathrm{x}}\right)^2+(1)^2+2 \times 2 \mathrm{x} \times \frac{1}{\mathrm{x}}+2 \times \frac{1}{\mathrm{x}} \times 1+2 \times 1 \times 2 \mathrm{x}$
$ =4 \mathrm{x}^2+\frac{1}{\mathrm{x}^2}+1+4+\frac{2}{\mathrm{x}}+4 \mathrm{x}$
$ =4 \mathrm{x}+\frac{1}{\mathrm{x}^2}+5+\frac{2}{\mathrm{x}}+4 \mathrm{x}$
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