若2x+y=0,则代数式4x3+2xy(x+y)+y3的值为_.

问题描述:

若2x+y=0,则代数式4x3+2xy(x+y)+y3的值为______.

∵2x+y=0,
∴4x3+2xy(x+y)+y3
=2x[2x2+y(x+y)]+y3
=2x[x(2x+y)+y2]+y3
=2xy2+y3
=y2(2x+y)
=0.
故答案为:0.