Consider 3-digit number as abc.
Follow these steps to better understand:
Step 1: get c2 by multiplying right side digits [cxc]
Step 2: get 2bc by criss-cross product of b and c [bxc+bxc=2bc]
Step 3: get 2ac+b2 by criss-cross product of a and c, criss cross product of middle digits b and b [axc+axc+bxb]
Step 4: get 2ab by criss-cross product of a and b [axb+axb]
Step 5: get a2 by multiplying right side digits [axa]
This can be written as:
Step 1: Break the number such that a=7, b=1 and c=3
Step 2: Compute a2, ab, ac, bc and c2 and write as shown in the updated formula.
Step 3: Notice the second row of the formula is obtained by repeating the second, third and fourth term
Step 4: Compute b2 and place it in the 3rd column below ac term.
Step 5: Now, add the terms taking care of the carry-forward in each step to obtain the square of the number.
So, 7132 = 508369