I assume you mean Arthur Benjamin?
The answer is yes. However; the method you quote is not Arthur Benjamin’s.
Let me explain.
If you want to use Arthur Benjamin’s method, you want to do it this way:
65x34 =
34x65 = (lowest number first)
(34-4) x (65+4) + 4 x (65-30) = (first goes down, second goes up, add the difference: 4, times the other difference(65-30=35))
30 x 69 + 4 x 35 = (30 x 69: easier is: 30 x 70- 30)
(2100 - 30) + (140)
2100 + 110 =
2210
Now with 3x3 it becomes a bit more complicated, involved and maybe taxing on the brain.
An easy example:
343x657 =
340 x 660 + 3 x (657-340) =
340 x 660 + 3 x 317 = (I’ll show you how I calculate 34 X 66)
500^2 - 160^2 + 951 =
250,000 - 25,600 + 951 = (-25,600 + 951 = -25,000 - 600 + 1,000 - 49 = -25,000 +351)
250,000 - 25,000 + 351 =
225,351
For 34 X 66 I use difference of squares. You can also fall back to any other 2x2 method.
In the previous example, when we take the 343 down to 340, the 657 became 660. This effectively makes it a 2x2.
A more general example would go like this:
343x653 =
340 x 656 + 3 x (653 - 340)=
340 x (660 - 4) + 3 x 313 =
340 x 660 - 4 x 340 + 3 x 313 =
500^2 - 160^2 - (3 X (340-313) - 340) =
250,000 - 25,600 - 3 x 27 - 340 =
224,400 - 421 =
223,979
Is this what you mean?
Or are you looking for different ways of calculating 3x3’s?