# Sophie Germain Identity

The Sophie Germain identity is a remarkable polynomial factorization. It is frequently useful in math contests, competitions, and olympiads. One would not expect this polynomial to factor, but an ingenious trick via the difference of squares factorization allows for the factorization $$x^4+4y^4 = (x^2-2xy+2y^2)(x^2+2xy+y^2).$$