Expand the following:
$\left(\frac{1}{x}+\frac{y}{3}\right)^{3}$
By acute division, find the quotient and the remainder when the first polynomial is divided by the second polynomial: $x^{4}+1 ; x+1$
Evaluate
$(101)^{2}$
Factorise
$16 x^{2}+40 x y+25 y^{2}$
Without actually calculating the cubes, find the value of each of the following
$(31)^{3}-(16)^{3}-(15)^{3}$