What method of factorization is this?

[autodidude]

$$x^4+1$$
$$x^4+2x^2+1-2x^2$$
$$(x^2+1)^2-(\sqrt{2}x)^2$$
$$(x^2+\sqrt{2}x+1)(x^2-\sqrt{2}x+1)$$

In particular the second line, seems obvious now that I've seen it but I've never come across in a book before - what is it called?

 

[mathman]

Completing the square?