Difference of Squares in Mental Arithmetic

One of the first tricks taught in factoring polynomials is the difference of squares formula, namely:

$x^2-y^2=(x+y)(x-y).$

This simple formula comes in handy in mental arithmetic when we substitute $x$ and $y$ with numbers, especially when you have your square numbers memorized. For example, suppose someone asks you to calculate 27 X 23. Here's a quick way to do this: Let $x=25$ and $y=2$ in the above formula. Then we get $25^2-2^2=(27)(23)$ . So the desired product is just the difference between $25^2$ and $2^2$ , which is $625-4=621$ .