Đáp án:
$\begin{array}{l}
a){\left( {{a^2} - {b^2}} \right)^2} + {\left( {2ab} \right)^2}\\
= {a^4} - 2{a^2}{b^2} + {b^4} + 4{a^2}{b^2}\\
= {a^4} + 2{a^2}{b^2} + {b^4}\\
= {\left( {{a^2} + {b^2}} \right)^2}\\
b)\left( {{a^2} + {b^2}} \right)\left( {{c^2} + {d^2}} \right)\\
= {a^2}{c^2} + {a^2}{d^2} + {b^2}{c^2} + {b^2}{d^2}\\
{\left( {ac + bd} \right)^2} + {\left( {ad - bc} \right)^2}\\
= {a^2}{c^2} + 2abcd + {b^2}{d^2} + {a^2}{d^2} - 2abcd + {b^2}{c^2}\\
= {a^2}{c^2} + {a^2}{d^2} + {b^2}{c^2} + {b^2}{d^2}\\
\Rightarrow \left( {{a^2} + {b^2}} \right)\left( {{c^2} + {d^2}} \right) = {\left( {ac + bd} \right)^2} + {\left( {ad - bc} \right)^2}
\end{array}$
