What method of factorization is this?

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    Factorization Method
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SUMMARY

The discussion centers on the factorization of the polynomial expression x^4 + 1 and its manipulation through completing the square. The transformation x^4 + 2x^2 + 1 - 2x^2 leads to the expression (x^2 + 1)^2 - (\sqrt{2}x)^2, which is a difference of squares. This method ultimately results in the factors (x^2 + \sqrt{2}x + 1)(x^2 - \sqrt{2}x + 1). The technique used is indeed completing the square, a fundamental algebraic method.

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[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?
 
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