For the people who do not have the book, here is a spoiler.
Let’s say you need to calculate 43 X 77.
This can be rewritten as 40 X 80 + 3 X 37.
40 X 80 is easy: 3200.
3 X 37 is 111.
3200 + 111 =
3311
Another one:
41 X 61 =
Rewrite to 40 X 62 + 1 X 21 =
2480 + 21 =
2501
49^2 =
50 X 48 + 1 =
2400 + 1 =
2401
51^2 =
50 X 52 + 1 =
2600 + 1 =
2601
It’s the rewrite that makes the calculation easier.