Using a suitable identity,evaluate the following:
$999^{2}$

Evaluate $(555)^{2}$.

With the help of the remainder theorem,find the remainder when the polynomial $p(x) = x^{3} + x^{2} - 26x + 24$ is divided by the divisor $x - 4$.

Find the quotient and the remainder when $x^{3}+x^{2}-10x+8$ is divided by $x+4$.

For the polynomial $\frac{x^{3}+2 x+1}{5}-\frac{7}{2} x^{2}-x^{6},$ write:
$(i)$ the degree of the polynomial
$(ii)$ the coefficient of $x^{3}$
$(iii)$ the coefficient of $x^{6}$
$(iv)$ the constant term

If $x = 2y + 6$,then what is the value of $x^3 - 8y^3 - 36xy - 216$?