Fast multiplication n-digits (on certain situations)

I've found a solution for fast multiplication n digits with respect to the following conditions:

• have the same number of digits

• the first digit of both numbers are equal

• the sum of last digit of both numbers is 10

Example for applicable numbers could be: 56 x 54, 21 x 29, 37 x 33, 112 x 118, etc. The algorithm: 56 x 54:

• the next ordinal number that comes after that 5 is 6; so we multiply 5x6 = 30, so we got the first two digits of our product

• the last step is to multiply the units numbers, I mean: 6 x 4 which is 24; so 24 is the last two digits of our product

This mean that 56 x 54 = 3024. Another example: 21 x 29:

• the next ordinal number that comes after that 2 is 3; so we multiply 2x3 = 6, so we got the first two digits of our product

• the last step is to multiply the units numbers, I mean: 1 x 9 which is 9; because is small than 10 we write down 09 instead of 9

This mean that 21 x 29 = 609. Another example: 112 x 118:

• the next ordinal number that comes after that 11 is 12; so we multiply 12x11 = 132, so we got the first two digits of our product

• the last step is to multiply the units numbers, I mean: 2 x 8 which is 16

This mean that 112 x 118 = 13216. When the above conditions are not meet you can still use the other method explained here and here.