Field/2 not 0/Product with squares/Explicit/Exercise

Let ${}K$ be a field with ${}2\neq 0$. Show that for ${}f,g\in K$ the relation

${}fg={\frac {1}{4}}{\left({\left(f+g\right)}^{2}-{\left(f-g\right)}^{2}\right)}\,$

holds.

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