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= xyx + xyy - yzy + yzz - zx( z - x )
= y( x^2 + xy ) - y( zy + zz ) - zx( z - x )
= y[ ( x^2 + xy ) - ( zy + zz ) ] - zx( z - x )
= y( x^2 + xy - zy - zz ) - zx( z - x )
= y[ x( x + y ) - z( y - z ) ] - zx( z - x )
P/S : bí rùi . ngu phần này lắm .
Đa thức trên tương đương với đa thức:
\(\left(xy\left(x+y\right)+xyz\right)+\left(yz\left(y+z\right)+xyz\right)+\left(xz\left(x+z\right)+xyz\right)\)
=\(xy\left(x+y+z\right)+yz\left(x+y+z\right)+xz\left(x+y+z\right)\)
=\(\left(x+y+z\right)\left(xy+yz+xz\right)\)
xy(x + y) + yz( y + z )+ zx( z + x ) + 3xyz
=xy(x + y) + xyz + yz(y + z) + xyz + xz(x + z)+xyz
=zy(x + y + z) + yz(x + y + z) + xz(x + y + z)
=(x + y + z)(xy + yz + zx)
chúc bn hok tốt
\(xyz-\left(xy+yz+xz\right)+\left(x+y+z\right)-1\)
\(=\left(xyz-xy-xz+x\right)-yz+y+z-1\)
\(=x\left(yz-y-z+1\right)-\left(yz-y-z+1\right)\)
\(=\left(x-1\right)\left(yz-y-z+1\right)\)
\(=\left(x-1\right)\left[y\left(z-1\right)-\left(z-1\right)\right]\)
\(=\left(x-1\right)\left(y-1\right)\left(z-1\right)\)
\(A=\left(x^2+y^2+z^2\right)\left(x+y+z\right)^2-\left(xy+yz+zx\right)^2\left(1\right)\)
Đặt \(x^2+y^2+z^2=a\)
\(xy+yz+zx=b\Rightarrow2\left(xy+yz+zx\right)=2b\)
\(\Rightarrow a+2b=\left(x+y+z\right)^2\)
Kết hợp (1) ta được : \(A=a\left(a+2b\right)+b^2\)
\(=a^2+2ab+b^2\)
\(=\left(a+b\right)^2\)
\(=\left(x^2+y^2+z^2+xy+yz+zx\right)^2\)
a) xy(x + y) + yz(y + z) + xz(z + x) + 3xyz
= xy(X + y + z) + yz(x + y + z) + xz(X + y + z)
= (x + y +z)(xy + yz+ xz)
b) xy(x + y) - yz(y + z) - xz(z - x)
= x2y + xy2 - y2z - yz2 - xz2 + x2z
= x2(y + z) - yz(y + z) + x(y2 - z2)
= x2(y + z) - yz(y + z) + x(y + z)(y - z)
= (y + z)(x2 - yz + xy - xz)
= (y + z)[x(x + y) - z(x + y)]
= (y + z)(x + y)(x - z)
c) x(y2 - z2) + y(z2 - x2) + z(x2 - y2)
= x(y - z)(y + z) + yz2 - yx2 + x2z - y2z
= x(y - z)(y + z) - yz(y - z) - x2(y - z)
= (y - z)((xy + xz - yz - x2)
= (y - z)[x(y - x) - z(y - x)]
= (y - z)(x - z)(y -x)
Ta có P = xyz - xy - yz - zx + x + y + z - 1
= (xyz - xy) - z(x + y) + (x + y) + (z - 1)
= xy(z - 1) - (x + y)(z - 1) + (z - 1)
= (z - 1)(xy - x - y + 1)
= (z - 1)[x(y - 1) - (y - 1)]
= (x - 1)(y - 1)(z - 1)
`Answer:`
`xyz-(xy+yz+zx)+(x+y+z)-1`
`=xyz-xy-yz-zx+x+y+z-1`
`=(xyz-xy)-(yz-y)-(zx-x)+(z-1)`
`=xy(z-1)-y(z-1)-x(z-1)+(z-1)`
`=(z-1)(xy-y-x+1)`
`=(z-1)[(xy-y)-(x-1)]`
`=(z-1)[(y(x-1)-(x-1)]`
`=(z-1)(x-1)(y-1)`
`=(x-1)(y-1)(z-1)`