I probably should have stopped while ahead but I wanted to include Art Benjamin’s method of squaring 2 digit numbers in the list of Anker techniques. I doubt he invented it but it often goes by his name.
Starting with the result we had before, the identity
(A+d)(A-d) = A2 - d2
Shift terms back and forth across the =
A2= (A+d)(A-d) + d2
Choose A to be the number to be squared, Choose d to bring one of the terms to a multiple of 10
632=(63-3)(63+3) + 32
...=60*66+9 =3969 <-- do not know why the editor impose this styling on this line
272= (27-3)(27+3) + 32 = 24*30+9 = 729