(x + y)2 = x2 + 2xy + y2
(x – y)2 = x2 – 2xy + y2
x2 – y2 = (x + y) (x – y)
(x + a) (x + b) = x2 + (a + b)x + ab.
(x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx
(x + y)3 = x3 + y3 + 3xy(x + y)
(x – y)3 = x3 – y3 – 3xy(x – y)
x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz – zx)
x3 + y3 = (x + y)(x2 - xy + y2)
x3 - y3 = (x-y)(x2 + xy + y2)