若2x+y=0,则代数式4x³+2xy(x+y)+y³的值为__
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/22 09:28:07
![若2x+y=0,则代数式4x³+2xy(x+y)+y³的值为__](/uploads/image/z/568579-67-9.jpg?t=%E8%8B%A52x%2By%3D0%2C%E5%88%99%E4%BB%A3%E6%95%B0%E5%BC%8F4x%26%23179%3B%2B2xy%28x%2By%29%2By%26%23179%3B%E7%9A%84%E5%80%BC%E4%B8%BA__)
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