Without actually calculating the cubes, find the value of each of the following

$\left(\frac{1}{2}\right)^{3}+\left(\frac{1}{3}\right)^{3}-\left(\frac{5}{6}\right)^{3}$

Find $p(-2)$ for the polynomial $p(x)=5 x^{2}-11 x+3$

Expand the following:

$\left(\frac{1}{x}+\frac{y}{3}\right)^{3}$

Without actual division, prove that $2 x^{4}-5 x^{3}+2 x^{2}-x+2$ is divisible by $x^{2}-3 x+2$

Check whether $p(x)$ is a multiple of $g(x)$ or not :

$p(x)=2 x^{3}-11 x^{2}-4 x+5, \quad g(x)=2 x+1$