Difference of Squares in Mental Arithmetic

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

This simple formula comes in handy in mental arithmetic when we substitute and 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 and in the above formula. Then we get . So the desired product is just the difference between and , which is .