Chứng minh (x^2 + y^2)^2 - (2xy)^2 = (x + y)^2 (x - y)^2

\({\left( {{x^2} + {y^2}} \right)^2} - {\left( {2xy} \right)^2} = {\left( {x + y} \right)^2}{\left( {x - y} \right)^2}\)

Ta có \({\left( {{x^2} + {y^2}} \right)^2} - {\left( {2xy} \right)^2} = \left( {{x^2} + {y^2} + 2xy} \right)\left( {{x^2} + {y^2} - 2xy} \right)\)

= (x + y)² (x – y)²