已知x+y=0,求x^3+x^2*y+xy^2+y^3

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已知x+y=0,求x^3+x^2*y+xy^2+y^3
已知x+y=0,求x^3+x^2*y+xy^2+y^3

已知x+y=0,求x^3+x^2*y+xy^2+y^3
x^3+x^2*y+xy^2+y^3
=（x^3+x^2*y）+（xy^2+y^3）
=x^2（X+y）+Y^2(X+Y)
因为X+y=0
所以原试的值为0

x+y=0
y=-x
x^3+x^2*y+xy^2+y^3
=x^3+x^2*(-x)+x(-x)^2+(-x)^3
=x^3-x^3+x^3-x^3
=0

因为X+y=0,得y=-x
x^3+x^2*y+xy^2+y^3
=x^3+x^3+x^3-x^3
=x^6

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