Difference of two squares

In elementary algebra, a difference of two squares is one squared number (the number multiplied by itself) subtracted from another squared number. Every difference of squares may be factored as the product of the sum of the two numbers and the difference of the two numbers:

$${\displaystyle a^{2}-b^{2}=(a+b)(a-b).}$$

Note that ${\displaystyle a}$ and ${\displaystyle b}$ can represent more complicated expressions, such that the difference of their squares can be factored as the product of their sum and difference. For example, given ${\displaystyle a=2mn+2}$, and ${\displaystyle b=mn-2}$ :

$${\displaystyle a^{2}-b^{2}=(2mn+2)^{2}-(mn-2)^{2}=(3mn)(mn+4).}$$

In the reverse direction, the product of any two numbers can be expressed as the difference between the square of their average and the square of half their difference:

$${\displaystyle xy=\left({\frac {x+y}{2}}\right)^{2}-\left({\frac {x-y}{2}}\right)^{2}.}$$