Sophie Germain identity

The polynomial identity

a^{4} + 4 b^{4} = (a^{2} - 2 ab + 2 b^{2}) (a^{2} + 2 ab + 2 b^{2})

follows by writing the left side as

(a^{2} + 2 b^{2})^{2} - (2 ab)^{2}

and taking a difference of squares.

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