\(x^3+x^2y-x^2z-xyz\)
\(=\left(x^3+x^2y\right)-\left(x^2z+xyz\right)\)
\(=x^2\left(x+y\right)-xz\left(x+y\right)\)
\(=\left(x^2-xz\right)\left(x+y\right)\)
\(=x\left(x-z\right)\left(x+y\right)\)
\(---\)
\(xa+xb+ya+yb-za-zb\)
\(=\left(xa+xb\right)+\left(ya+yb\right)-\left(za+zb\right)\)
\(=x\left(a+b\right)+y\left(a+b\right)-z\left(a+b\right)\)
\(=\left(x+y-z\right)\left(a+b\right)\)
\(---\)
\(x^2-4xy+4y^2-x+2y\)
\(=\left(x^2-4xy+4y^2\right)-\left(x-2y\right)\)
\(=\left[x^2-2\cdot x\cdot2y+\left(2y\right)^2\right]-\left(x-2y\right)\)
\(=\left(x-2y\right)^2-\left(x-2y\right)\)
\(=\left(x-2y-1\right)\left(x-2y\right)\)
\(---\)
\(xz-yz-x^2+2xy-y^2\)
\(=\left(xz-yz\right)-\left(x^2-2xy+y^2\right)\)
\(=x\left(x-y\right)-\left(x-y\right)^2\)
\(=\left(x-y\right)\left[x-\left(x-y\right)\right]\)
\(=\left(x-y\right)\left(x-x+y\right)\)
\(=\left(x-y\right)y\)
#\(Toru\)
