x^4+y^4=50 x^2y-xy^2=-14 求代数式x^4- y^4+3xy^2-xy^2-5x^2y+3x^2y-2y^4的值

题有错吧。因该是+2y^4吧

x^4- y^4+3xy^2-xy^2-5x^2y+3x^2y+2y^4
=x^4+ y^4+2xy^2-2x^2y
=50-2*(-14)
=78

-14=x^2y-xy^2=xy(x-y)

x^4- y^4+3xy^2-xy^2-5x^2y+3x^2y-2y^4
=x^4-3y^4+2xy^2-2x^2y
=x^4-3y^4-2xy(x-y)

题目最后一项会不会是+2y^4？
这样，上式=x^4+y^4-2xy(x-y)=50-2*（-14）=78

x^4- y^4+3xy^2-xy^2-5x^2y+3x^2y+2y^4
=x^4+ y^4+2xy^2-2x^2y
=50-2*(-14)
=78