What method of factorization is this?

autodidude

[tex]x^4+1[/tex]
[tex]x^4+2x^2+1-2x^2[/tex]
[tex](x^2+1)^2-(\sqrt{2}x)^2[/tex]
[tex](x^2+\sqrt{2}x+1)(x^2-\sqrt{2}x+1)[/tex]

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?