Question

[Lelemalin]

Phân tích đa thức thành nhân tử:

xyz - (xy + yz + zx) + x + y + z -1

Answer 1

[Nguyễn Việt Lâm]

\(=xyz-xy-z\left(x+y\right)+x+y+z-1\)

\(=xy\left(z-1\right)-\left(x+y\right)\left(z-1\right)+z-1\)

\(=\left(z-1\right)\left(xy-x-y+1\right)\)

\(=\left(z-1\right)\left[x\left(y-1\right)-\left(y-1\right)\right]\)

\(=\left(x-1\right)\left(y-1\right)\left(z-1\right)\)