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Algebra Difficulty 6.0 National olympiad Prove it

4. 证明: (i) (a2+b2)(c2+d2)=(ac+bd)2+(ad−bc)2\left(a^{2}+b^{2}\right)\left(c^{2}+d^{2}\right)=(a c+b d)^{2}+(a d-b c)^{2};
(ii) (a2−b2)(c2−d2)=(ac+bd)2−(ad+bc)2\left(a^{2}-b^{2}\right)\left(c^{2}-d^{2}\right)=(a c+b d)^{2}-(a d+b c)^{2}.

Solution

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