作业帮若x+y=-1,则x^4+5x^3y+x^2y+8x^2y^2+xy^2+5xy^3+y^4=( )
来源：学生作业帮 编辑：拍题作业网作业帮 分类：数学作业 时间：2024/04/28 01:25:33
若x+y=-1,则x^4+5x^3y+x^2y+8x^2y^2+xy^2+5xy^3+y^4=( )
若x+y=-1,则x^4+5x^3y+x^2y+8x^2y^2+xy^2+5xy^3+y^4=( ）
若x+y=-1,则x^4+5x^3y+x^2y+8x^2y^2+xy^2+5xy^3+y^4=( ）
=(x^4+x^3y)+(y^4+xy^3)+(4x^3y+4x^2y^2)+(4xy^3+4x^2y^2)+x^2y+xy^2
=x^3(x+y)+y^3(x+y)+4x^2y(y+x)+4xy^2(y+x)+x^2y+xy^2
=-x^3-y^3-4x^2y-4xy^2+xy^2+x^2y
=-x^3-y^3-3x^2y-3xy^2
=-(x^3+x^2y)-(y^3+xy^2)-2x^2y-2xy^2
=-x^2(x+y)-y^2(x+y)-2xy(x+y)
=x^2+y^2+2xy
=(x+y)^2
=1
=x^3(x+y)+y^3(x+y)+4x^2y(y+x)+4xy^2(y+x)+x^2y+xy^2
=-x^3-y^3-4x^2y-4xy^2+xy^2+x^2y
=-x^3-y^3-3x^2y-3xy^2
=-(x^3+x^2y)-(y^3+xy^2)-2x^2y-2xy^2
=-x^2(x+y)-y^2(x+y)-2xy(x+y)
=x^2+y^2+2xy
=(x+y)^2
=1
若x+y=-1,则x^4+5x^3y+x^2y+8x^2y^2+xy^2+5xy^3+y^4=( )
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