Identity I    : (x + y)²= x² + 2xy + y²

Identity II   : (x – y)² = x²  – 2xy + y² 

Identity III  : x² – y²= (x + y) (x – y) 

Identity IV  : (x + a) (x + b) = x²+ (a + b)x + ab

Identity V   : (x + y + z)² = x²+ y²+ z² + 2xy + 2yz + 2zx

Identity VI  : (x + y)³ = x³ + y³+ 3xy (x + y) 

Identity VII : (x – y)³ = x³ – y³ – 3xy(x – y) = x³ – 3x²y + 3xy² – y³

Identity VIII : x³ + y³ + z³ – 3xyz = (x + y + z)(x² + y² + z² – xy – yz – zx)