\[\begin{array}{l}{\text{Разложите многочлен }}4{x^4} + {y^4}{\text{ в произведение}}\\{\text{двух многочленов с целыми коэффициентами}}{\text{.}}\end{array}\]
\[{a^2} + {b^2} = {\left( {a + b} \right)^2} - 2ab\]
\[\begin{array}{l}4{x^4} + {y^4} = {\left( {2{x^2}} \right)^2} + {\left( {{y^2}} \right)^2} = {\left( {2{x^2} + {y^2}} \right)^2} - 2 \cdot 2{x^2} \cdot {y^2} = \\{\left( {2{x^2} + {y^2}} \right)^2} - {\left( {2xy} \right)^2} = \left( {2{x^2} + {y^2} - 2xy} \right)\left( {2{x^2} + {y^2} + 2xy} \right)\end{array}\]
\[4{x^4} + {y^4} = \left( {2{x^2} + {y^2} - 2xy} \right)\left( {2{x^2} + {y^2} + 2xy} \right)\]
