If $x-\frac{1}{x}=11$, find the values of $x^2+\frac{1}{x^2}$ and $x^4+\frac{1}{x^4}$.

If $3x-5y=1$ and $xy=6$, find the value of $9x^2+25y^2$

Find the value of the following expression.

$9x^2+24x+16$ when $x=\frac{5}{3}$

Find the value of the following expression.

$25x^2-60xy+36y^2$ when $x=\frac{2}{5}$ and $y=\frac{5}{3}$

What must be added to the following expression to make it a perfect square.

$25x^2-70x+7$

What must be added to the following expression to make it a perfect square.

$4x^2-60x+15$

Simplify:

$\left(x+1\right)\left(x-1\right)\left(x^2+1\right)\left(x^4+1\right)$