х¹⁶ - у¹⁶ =(х+у)(х²+у²)(х⁴+у⁴)(х⁸+у⁸)
х-у
1) х¹⁶-у¹⁶=(х⁸-у⁸)(х⁸+у⁸)=(х⁴-у⁴)(х⁴+у⁴)(х⁸+у⁸)=(х²-у²)(х²+у²)(х⁴+у⁴)(х⁸+у⁸)=
=(х-у)(х+у)(х²+у²)(х⁴+у⁴)(х⁸+у⁸)
2) (х-у)(х+у)(х²+у²)(х⁴+у⁴)(х⁸+у⁸) = (х+у)(х²+у²)(х⁴+у⁴)(х⁸+у⁸)
х-у
(х+у)(х²+у²)(х⁴+у⁴)(х⁸+у⁸)=(х+у)(х²+у²)(х⁴+у⁴)
-y^8=-y^8
Тождество верно
Объяснение:
(ху+х²-y²-xy)(x²+y²)(x⁴+y⁴)-x^8=-y^8
(x⁴+x²y²-x²y²-y⁴)(x⁴+y⁴) - x^8=-y^8
x^8+x⁴y⁴-x⁴y⁴-y^8-x^8=-y^8
-y^8=-y^8
