If $x+\frac{1}{x}=11$, find the value of $x^2+\frac{1}{x^2}$

If $\left(x-\frac{1}{x}\right)=5$ find the values of $\left(x^2+\frac{1}{x^2}\right)$ and $\left(x^4+\frac{1}{x^4}\right)$.

Find the value of the expression $(36x^2+25y^2–60xy)$ when $x=\frac{2}{3}$and $y=\frac{1}{5}$.

Find the continued product of $(x+ 1)(x–1)(x^2+1)$.

Find the value of the expression $(9x^2+24x+16)$, when $x=12$.

If $\mathrm{x}+\mathrm{y}=12$ and $\mathrm{xy} = 14$, find the value of $({\mathrm{x}}^2+{\mathrm{y}}^2)$.

Using the formula for squaring a binomial, evaluate $(54{)}^2$.

Using the formula for squaring a binomial, evaluate ${\left(69\right)}^2$.

Find the value of the expression $(64x^2+81y^2+144xy)$, when $x=11$ and $y=\frac{4}{3}$.

If $\left(x+\frac{1}{x}\right)=4$ find the value of $\left(x^2+\frac{1}{x^2}\right)$ and $\left(x^4+\frac{1}{x^4}\right)$

Find the value of $(82{)}^2–(18{)}^2$.