Identity I : $(x + y)^2$ = $x^2 + 2xy + y^2$ 

Identity II : $(x - y)^2$ = $x^2 - 2xy + y^2$ 

Identity III : $x^2 - y^2$ = $(x + y) (x - y)$ 

Identity IV : $ (x + a) (x + b) = x^2 + (a + b)x + ab $ 

Identity V : $(x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx $

Identity VI : $(x + y)^3 = x^3 + y^3 + 3xy (x + y)$

Identity VII : $(x – y)^3 = x^3 – y^3 – 3xy(x – y)$

              = $x^3 – 3x^2y + 3xy^2 – y^3$

Identity VIII : $x^3 + y^3 + z^3 – 3xyz = (x + y + z)(x^2 + y^2 + z^2 – xy – yz – zx)$