Factored Form  Product  This is called a 
(x + y)²  x² +2xy + y²  perfect square trinomial 
(x  y)²  x²  2xy + y²  perfect square trinomial 
x^{3}  y^{3}  (x  y)(x² + xy + y²)  difference of two cubes 
x^{3} + y^{3}  (x + y)(x²  xy + y²)  sum of two cubes 
x²  y²  (x  y)(x + y)  difference of two squares 
x² + y² *  (x yi)(x + yi), i = (1)  sum of two squares 
* This expression can't be factored over the reals but can be factored over the complex numbers.
For vocabulary, see What Do You Call A Hungry Parrot? Lesson, 220.
For general guidelines and animations on factoring see Written Notes on Factoring or other notes below.

www.mathnstuff.com/math/spoken/here/2class/290/c29pg00.htm 