Difference of Two Squares

The difference of two squares is an algebraic identity describing what happens when one squared quantity is subtracted from another. It states that for any two numbers or expressions a and b, a squared minus b squared always factors as the product of their sum and their difference, that is, as the quantity a plus b times the quantity a minus b. The two quantities a and b need not be simple numbers; they can themselves be more complicated expressions, and the identity still lets their squared difference be factored the same way. Run in the opposite direction, the identity also shows that the product of any two numbers can be written as the square of their average minus the square of half their difference, a fact used in a variety of algebraic manipulations and mental arithmetic shortcuts.