1樓:匿名使用者
^^^^是x^du3+y^zhi3+z^3-3xyz嗎?
x^3+y^dao3+z^3-3xyz=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)
由x^3+y^3+z^3
=(x+y+z)(x^2+y^2+z^2)內-z(容x^2+y^2)-x(y^2+z^2)-y(x^2+z^2)x^3+y^3+z^3-3xyz=......=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)
x^3+y^3+z^3-3xyz因式分解
2樓:網際超人
= (x^3+3yx^2+3xy^2+y^3)+z^3-3xyz-3yx^2-3xy^2
= (x+y)^3+z^3-3xy(x+y+z)= (x+y+z)[(x+y)^2-(x+y)z+z^2]-3xy(x+y+z)
= (x+y+z)[(x^2+2xy+y^2-xz-yz+z^2)-2xy]
= (x+y+z)(x^2+y^2+z^2-xy-yz-zx)不懂還可問,滿意請及時採納!o(∩_∩)o
因式分解(x+y+z)^3-x^3-y^3-z^3
3樓:小賤
^參考下面
(x+y+z)^3-x^3-y^3-z^3=3yx^2+3xy^2+3xz^2+3yz^2+3zx^2+3zy^2+6xyz
=3xy(x+y)+3z^2(x+y)+3z(x^2+y^2+2xy)
=3xy(x+y)+3z^2(x+y)+3z(x+y)^2=3(x+y)[xy+z^2+z(x+y)]=3(x+y)[x(y+z)+z(y+z)]=3(x+y)(x+z)(y+z)、
、好評,,o(∩_∩)o謝謝
x^3+y^3+z^3-xyz如何分解因式
4樓:我不是他舅
x3+y3+z3-3xyz
=(x3+3x2y+3xy2+y3+z3)-(3xyz+3x2y+3xy2)
=[(x+y)3+z3]-3xy(x+y+z)=(x+y+z)(x2+y2+2xy-xz-yz+z2)-3xy(x+y+z)
=(x+y+z)(x2+y2+z2+2xy-3xy-xz-yz)=(x+y+z)(x2+y2+z2-xy-yz-xz)
x^3+y^3+z^3-3xyz因式分解
5樓:匿名使用者
x3+y3+z3-3xyz
=(x+y+z)(x2+y2+z2-xy-xz-yz)
(這用到的是公式a3+b3+c3-3abc=(a2+b2+c2-ab-ac-bc))
6樓:虎慈建萍韻
^^^x^3+y^3+z^3-3xyz
=(x^3+3yx^2+3xy^2+y^3)+z^3-3xyz-3yx^2-3xy^2
=(x+y)^3+z^3-3xy(x+y+z)=(x+y+z)[(x+y)^2-(x+y)z+z^2]-3xy(x+y+z)
=(x+y+z)[(x^2+2xy+y^2-xz-yz+z^2)-2xy]
=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)
因式分解:x^2(y+z)+y^2(z+x)+z^2(x+y)-(x^3+y^3+z^3)-2xyz 10
7樓:一朵不知所云
^^^^x^2(y+z)+y^2(z+x)+z^2(x+y)-(x^3+y^3+z^3)-2xyz
=x^2(y+z)+y^2*z+y^2*x+z^2*x+z^2*y-x^3-y^3-z^3-2xyz
=x^2(y+z-x)+x(y^2+z^2-2yz)+(y^2*z+z^2*y-y^3-z^3)
=x^2(y+z-x)+x(y-z)^2+[y^2(z-y)-z^2(z-y)]
=x^2(y+z-x)+x(y-z)^2+(y+z)(y-z)(z-y)
=x^2(y+z-x)+x(y-z)^2-(y+z)(y-z)^2
=x^2(y+z-x)+(y-z)^2(x-y-z)
=(x-y-z)(z-y-x)(z-y+x)
若x+y+z=0,則分解因式x^3+y^3+z^3= 要過程詳細點 有什麼方法告訴我!!!急急急!!!求你了!
8樓:匿名使用者
你好,希望下面的答案對你有幫助
x+y+z=0則z=-(x+y)z
因式分解 x^2(y+z)+y^2(z+x)+z^2(x+y)-(x^3+y^3+z^3)-2xyz
9樓:匿名使用者
^^^^x^zhi2(y+z)+y^dao2(z+x)+z^回2(x+y)-(x^答3+y^3+z^3)-2xyz
=x^2(y+z)+y^2*z+y^2*x+z^2*x+z^2*y-x^3-y^3-z^3-2xyz
=x^2(y+z-x)+x(y^2+z^2-2yz)+(y^2*z+z^2*y-y^3-z^3)
=x^2(y+z-x)+x(y-z)^2+[y^2(z-y)-z^2(z-y)]
=x^2(y+z-x)+x(y-z)^2+(y+z)(y-z)(z-y)
=x^2(y+z-x)+x(y-z)^2-(y+z)(y-z)^2
=x^2(y+z-x)+(y-z)^2(x-y-z)
=(x-y-z)(z-y-x)(z-y+x)
10樓:匿名使用者
=x^2(y z-x) x(y-z)^2-(y z)(y-z)^2 =x^2(y z-x) (y-z)^2(x-y-z) =(x-y-z)(z-y-x)(z-y x)
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