早教吧作业答案频道 -->数学-->
分解因式:xy(x-y)+yz(y-z)+xz(z-x)
题目详情
分解因式:xy(x-y)+yz(y-z)+xz(z-x)
▼优质解答
答案和解析
原式=x^2*y - xy^2 +y^2*z -yz^2+xz^2-x^2*z(去括号)
=x^2*y -yz^2- xy^2 +y^2*z -x^2*z+xz^2(重新组合)
=y(x^2-z^2) -y^2(x-z)-xz(x-z)
=y(x-z)(x+z)-y^2(x-z)-xz(x-z)
=(x-z)(xy+yz-y^2-xz)
=(x-z)[y(x-y)-z(x-y)]
=(x-z)(x-y)(y-z)
=x^2*y -yz^2- xy^2 +y^2*z -x^2*z+xz^2(重新组合)
=y(x^2-z^2) -y^2(x-z)-xz(x-z)
=y(x-z)(x+z)-y^2(x-z)-xz(x-z)
=(x-z)(xy+yz-y^2-xz)
=(x-z)[y(x-y)-z(x-y)]
=(x-z)(x-y)(y-z)
看了分解因式:xy(x-y)+yz...的网友还看了以下：
化简(2x-y-z/x^2-xy-xz+yz)+(2y-x-z/y^2-xy-yz+xz)+(2x 2020-05-16 …
已知：xy/x+y=a,xz/x+z=b,yz/y+z=c.求证:x=2abc/bc+ac-ab. 2020-06-21 …
第一型曲面积分,这倒第一型曲面积分题,根本都没法下笔下一个字,函数是xy+yz+xz,积分曲面为圆 2020-08-03 …
已知xyz=1,求x/(xy+x+1)+y/(yz+y+1)+z/(xz+z+1)的值已知xyz=1 2020-10-31 …
x+y+1分之xy+x=2x+z+2分之xz+2x=3Y+z+3分之yz+2y+z+2=43个式子是 2020-10-31 …
xy+yz+xz=y+x+z之类的这种题叫做什么问题就是类似比如xy=x+y-9,yz=y+z-7, 2020-11-01 …
数列An=x^n+y^n+z^n的递推式是怎么证明的.An+3=(x+y+z)An+2-(xy+yz 2020-11-01 …
已知：xy/x+y=12,xz/x+z=15,yz/y+z=20.求x,y,z的值.应该是xy/(x 2020-11-01 …
若x,y,z∈（0,1）且xy+yz+xz=1求证y/(2-√3x)+z/(2-√3y)+若x,y, 2020-11-01 …
设x>0,y>0.z>0,且x+y+z=1⑴求证xy+yz+xz≤1⑵求（yz/x+xz/y+xy/ 2020-11-01 …