X^4+X^3+X^2Y+XY^2+Y^3-Y^4 =(X^4-Y^4)+(X^3+X^2Y)+(XY^2+Y^3) =(X^2+Y^2)(X^2-Y^2)+X^2(X+Y)+Y^2(X+Y) =(X^2+Y^2)(X+Y)(X-Y)+(X^2+Y^2)(X+Y) =(X^2+Y^2)(X+Y)(X-Y+1)
天啊，我来晚了一步~我一分钟就做出来来了，只是我去吃饭了。呵呵，但是我同意楼上的说法，第一个是错误的~~
x^4+x^3+x^2y+xy^2+y^3-y^4 =x^4-y^4+x^3+x^2y+xy^2+y^3 =(x^2+y^2)(x^2-y^2)+(x+y)(x^2+y^2) 注：x^3+x^2y+xy^2+y^3=(x+y)(x^2+y^2) =(x^2+y^2)(x+y)(x-y)+(x+y)(x^2+y^2) =(x^2+y^2)(x+y)(x-y+1)
X^4+X^3+X^2Y+XY^2+Y^3-Y^4 =(X^4-Y^4)+(X^3+Y^3)+(X^2Y+XY^2) =[(X^2-Y^2)(X^2+Y^2)]+[(X+Y)(X^2-XY+Y^2)]+XY(X+Y) =[(X-Y)(X+Y)(X^2+Y^2)]+[(X+Y)(X^2-XY+Y^2)]+XY(X+Y) =(X+Y)[(X-Y)(X^2+Y^2)+(X^2-XY+Y^2)+XY] =(X+Y)(X^2+Y^2)(X-Y+1)
X^4+X^3+X^2Y+XY^2+Y^3-Y^4 = =X^4-Y^4 +X^3+X^2Y+XY^2+Y^3= =(X^2-Y^2)(X^2+Y^2)+(X^4-Y^4)/(X-Y)= =(X^2+Y^2)(X^2-Y^2+X+Y)=(X^2+Y^2)(X+Y)(X-Y-1).
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