Hi MathsisFun;

Good page. Helped me a lot with the geometric representation.

Those 3 basic forms

(a+b)(a+b)
(a-b)(a-b)
(a+b)(a-b)

are also the basis for mental arithmetic. Lets take your example:

If you wanted to multiply 38 * 42 you could use that form with y=10.
Answer 16*100 - 4 = 1596 like magic.

For 63 * 57

63*57 = 36 * 100 -9 = 3591

With a little practice and algebra, you can do lots of arithmetic in your head.