# Part 2vi: Area Model of Multiplication

### Further Explanation for this Clip:

**Mentally Computing Two-Digit Squares**

In the previous clip I discussed how to use the identity to mentally compute two-digit squares such as , but I never got around to demonstrating how to do so. So here is a step-by-step explanation:

In order to use the identity, we need to think of as . Now we apply the above identity, with playing the role of , and playing the role of :

Notice that although there are several computations on the right hand side of the equation, they are all relatively simple mental math problems:

Therefore, .

Notice that there was nothing special about the number ; if you want to square any two-digit number, the ‘’ part of the computation will always be similar to our above computations. Since we are using expanded form, our ‘’ will always be a multiple of , and our ‘’ will always be a one-digit number; thus will always be the square of a multiple of (a relatively easy mental computation), will always be the product of two one-digit numbers ( and ) and a multiple of (again, a relatively easy mental computation), and will always be a one-digit square.

Try a few on your own, and once you have the hang of it you will be able to wow and amaze your friends and colleagues with your mental math prowess!