Recently came across this technique of multiplying two $2$-digit numbers involving the same digit at the tens place and the sum of digits at units place being $10$. E.g., $73 X 77$ has same digit at the tenth place, viz., $7$ and the sum of digits at the ones place is $7+3 = 10$.
As per the technique the easy way to solve this simply multiply the digits at ones place together which in the above case would be $7. 3 = 21$ and the digit at the tenth place by the next number, i.e., $7.8=56$ in the above. The final answer then becomes after concatenating the two answers thus obtained, and hence $73.77=5621$. Similarly, $68.62=4216$ obtained by multiplying $6.7=42$ and $8.2=16$ and concatenating the two to obtain $4216$.
Can anyone explain the math behind this seemingly simple math trick?