\[\boxed{\text{841.}\text{\ }еуроки - ответы\ на\ пятёрку}\]
\[(ac + bd)^{2} + (ad - bc)^{2} = a^{2}c^{2} + 2acbd + b^{2}d^{2} + a^{2}d^{2} - 2adbc + b^{2}c^{2} =\]
\[= a²c² + b²d² + a²d² + b²c²\]
\[\left( a^{2} + b^{2} \right)\left( c^{2} + d^{2} \right) = a^{2}c^{2} + a^{2}d^{2} + b^{2}c^{2} + b^{2}d^{2}\ \]
\[Следовательно:\]
\[(ac + bd)^{2} + (ad - bc)^{2} = \left( a^{2} + b^{2} \right)\left( c^{2} + d^{2} \right)\]