Classify the following as linear, quadratic and cubic polynomials :
$(i)$ $x^{2}+x$
$(ii)$ $x-x^{3}$
$(iii)$ $y+y^{2}+4$
Determine which of the following polynomials has $(x + 1)$ a factor : $x^{3}-x^{2}-(2+\sqrt{2}) x+\sqrt{2}$
Factorise of the following : $27 y^{3}+125 z^{3}$
Evaluate using suitable identities : $(999)^{3}$
Factorise $4 x^{2}+y^{2}+z^{2}-4 x y-2 y z+4 x z$.