求教两道因式分解题x^2y-y^2z+z^2x-x^2z+y^2x+z^2y-2xyzx^2-(m^2+n^2)x+mn
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求教两道因式分解题
x^2y-y^2z+z^2x-x^2z+y^2x+z^2y-2xyz
x^2-(m^2+n^2)x+mn(m^2-n^2)
注:^是平方
x^2y-y^2z+z^2x-x^2z+y^2x+z^2y-2xyz
x^2-(m^2+n^2)x+mn(m^2-n^2)
注:^是平方
1.分组
x^2y-y^2z+z^2x-x^2z+y^2x+z^2y-2xyz
=(x^2y-xyz)+(z^2x-x^2z) +(z^2y-y^2z)+(y^2x-xyz)
=xy(x-z)+xz(z-x)+yz(z-y)+xy(y-z)
=x(x-z)(y-z)+y(y-z)(x-z)
=(x-z)(y-z)(x+y)
2.十字相乘法
1 -m(m-n)
1 -n(m+n)
---------------
-(m^2+n^2)
从而
x^2-(m^2+n^2)x+mn(m^2-n^2)
=[x-m(m-n)][x-n(m+n)]
=(x-m^2+mn)(x-mn-n^2)
x^2y-y^2z+z^2x-x^2z+y^2x+z^2y-2xyz
=(x^2y-xyz)+(z^2x-x^2z) +(z^2y-y^2z)+(y^2x-xyz)
=xy(x-z)+xz(z-x)+yz(z-y)+xy(y-z)
=x(x-z)(y-z)+y(y-z)(x-z)
=(x-z)(y-z)(x+y)
2.十字相乘法
1 -m(m-n)
1 -n(m+n)
---------------
-(m^2+n^2)
从而
x^2-(m^2+n^2)x+mn(m^2-n^2)
=[x-m(m-n)][x-n(m+n)]
=(x-m^2+mn)(x-mn-n^2)
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