Given a quadratic form Q(x, y) congruent x^2 + y^2, then Q(x, y) Q(x', y') = Q(x x' - y y', x' y + x y'), since (x^2 + y^2)(x^(, 2) + y^(, 2)) | = | (x x' - y y')^2 + (x y' + x' y)^2 | = | x^2 x^(, 2) + y^2 y^(, 2) + x^(, 2) y^2 + x^2 y^(, 2).

genus theorem | quadratic form