已知x-y=2,xy=-1,求x^2y^4-4x^3y^3+x^4y^2的值

已知x-y=2,xy=-1,求x^2y^4-4x^3y^3+x^4y^2的值
已知x-y=2,xy=-1,求x^2y^4-4x^3y^3+x^4y^2的值

已知x-y=2,xy=-1,求x^2y^4-4x^3y^3+x^4y^2的值
x^2y^4-4x^3y^3+x^4y^2
=x^2y^2(y^2-2xy+x^2)-2x^3y^3
=x^2y^2(y-x)^2-2x^3y^3
=1*4-2*(-1)
=1*4+2
=4+2
=6