若x^4+y^4=25,x^2-xy^2=-6,求x^4-y^4+xy^2-x^2y+2y^4的值.

若x^4+y^4=25,x^2y-xy^2=-6,求x^4-y^4+xy^2-x^2y+2y^4的值
x^4-y^4+xy^2-x^2y+2y^4
=x^4+y^4+xy^2-x^2y
=x^4+y^4-(x^2y-xy^2)
=25-(-6)
=25+6
=31

若x⁴+y⁴=25，x²y-xy²=-6，求x⁴-y⁴+xy²-x²y+2y⁴的值。
(原题有错！应是x²y-xy²=-6，不是x²-xy²=-6)
x⁴-y⁴+xy²-x²y+2y⁴=x⁴+y⁴-(x²y-xy²)=25-(-6)=31