若2x+y=0,则代数式4x³+2xy(x+y)+y³的值为__

若2x+y=0,则代数式4x³+2xy(x+y)+y³的值为__
若2x+y=0,则代数式4x³+2xy(x+y)+y³的值为__

若2x+y=0,则代数式4x³+2xy(x+y)+y³的值为__
4x³+2xy(x+y)+y³
=8x^3+y^3-4x^3+2xy(x+y)
=(2x+y)(4x^2+y^2-2xy)-2x(2x^2-xy-y^2)
=-2x(2x^2-xy-y^2)
=-2x[x(2x+y)-xy-xy-y^2)]
=-2x[-xy-xy-y^2)]
=2xy(2x+y)
=0