4a^4 + b^4 = (a^2 + (a + b)^2))(a^2 + (a - b)^2))

Dickson notes that Sophie Germain has observed that 4a^4+b^4 has factors 2a^2 \pm2ab+b^2. This implies the above identity.

A couple of examples can be found on a separate page.


References