已知x-y=1,求多项式x的4次方-x三次方y-3x平方y+3xy平方-xy立方+y四次方.？
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x ^4 -xy-3xy+3xy-xy+y^4
=x(x-y)-y(x-y)-3xy(x-y)=(x-y)(x-y)-3xy(x-y) =(x-y)-3xy =(x-y)(x+xy+y)-3xy = x+xy+y-3xy =x-2xy+y= (x-y)=1,7,X^4-X^3Y-3X^2Y+3XY^2-XY^3+Y^4=X^3(X-Y)-3XY(X-Y)-Y^3(X-Y)=(X-Y)((X^3-3XY-Y^3)=X^3-3XY-Y^3=(X-Y)(X^2+XY+Y^2)-3XY=X^2+XY+Y^2-3XY=X^2-2XY+Y^2=(X-Y)^2=1.,2,
=x(x-y)-y(x-y)-3xy(x-y)=(x-y)(x-y)-3xy(x-y) =(x-y)-3xy =(x-y)(x+xy+y)-3xy = x+xy+y-3xy =x-2xy+y= (x-y)=1,7,X^4-X^3Y-3X^2Y+3XY^2-XY^3+Y^4=X^3(X-Y)-3XY(X-Y)-Y^3(X-Y)=(X-Y)((X^3-3XY-Y^3)=X^3-3XY-Y^3=(X-Y)(X^2+XY+Y^2)-3XY=X^2+XY+Y^2-3XY=X^2-2XY+Y^2=(X-Y)^2=1.,2,
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