Question

Find the square of ${\displaystyle 2\text{x}+\frac{1}{\text{x}}+1}$

Answer 1

${\displaystyle {(2\text{x}+\frac{1}{\text{x}}+1)}^2={\left(2\text{x}\right)}^2+{\left(\frac{1}{\text{x}}\right)}^2+{\left(1\right)}^2+2\times 2\text{x}\times \frac{1}{\text{x}}+2\times \frac{1}{\text{x}}\times 1+2\times 1\times 2\text{x}}$

${\displaystyle =4{\text{x}}^2+\frac{1}{{\text{x}}^2}+1+4+\frac{2}{\text{x}}+4\text{x}}$

${\displaystyle =4{\text{x}}^2+\frac{1}{{\text{x}}^2}+5+\frac{2}{\text{x}}+4\text{x}}$