\(\left(x+y\right)\left(x+z\right)\left(y+z\right)+xyz\)
Khai triển ra ta được:
\(=\left[xyz+\left(xy^2+yx^2\right)+\left(xz^2+zx^2\right)+\left(yz^2+zy^2\right)+xyz\right]+xzy\)
\(=\left[xyz+xy\left(x+y\right)+xz\left(x+z\right)+yz\left(y+z\right)+xyz\right]+xyz+A+B\)
\(A=\left(xy+xz+yz\right)\)và \(B=\left(-xy-xz-yz\right)\)
\(=\left[xy\left(x+y\right)+xy\right]+\left[xz\left(x+z\right)+xz\right]+\left[yz\left(y+z\right)+yz\right]+\left(xyz-xy\right)+\left(xyz-xz\right)+\left(xyz-yz\right)\)
\(=xy\left(x+y+1\right)+xz\left(x+z+1\right)+yz\left(y+z+1\right)+xy\left(z-1\right)+xz\left(y-1\right)+yz\left(x-1\right)\)
\(=xy\left(x+y+z\right)+xz\left(x+z+y\right)+yz\left(y+z+x\right)\)
\(=\left(x+y+z\right)\left(xy+yz+zx\right)\)
