ABSTRACT
The humble identity a 2 − b 2 = (a − b)(a + b) deserves more emphasis than it usually gets. This is probably because it is generally seen as part of algebra, viewed as an abstract formal game not clearly related to arithmetic. In text books it is included in the chapter on factorisation, and the exercises usually just practise variations like 64u 2 − 49v 2 or even (3x + y)2 − (x − 5y)2.
