因式分解：X^4+X^3+X^2Y+XY^2+Y^3-Y^4 請給出過程,謝謝!!

熱心網(wǎng)友

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)

熱心網(wǎng)友

天啊，我來晚了一步~我一分鐘就做出來來了，只是我去吃飯了。呵呵，但是我同意樓上的說法，第一個是錯誤的~~

熱心網(wǎng)友

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)

熱心網(wǎng)友

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)

熱心網(wǎng)友

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).