Factorise the following : (ii) \( y z(y-z)+z x(z-x)+x y(x-y) \) (ii) \( y z(y+z)+z x(z+x)+x y(x+y)+2 x y z \)

Factor the expression \( yz(y-z)+zx(z-x)+xy(x-y) \). Factor the expression by following steps: - step0: Factor: \(yz\left(y-z\right)+zx\left(z-x\right)+xy\left(x-y\right)\) - step1: Simplify: \(y^{2}z-yz^{2}+zx\left(z-x\right)+xy\left(x-y\right)\) - step2: Simplify: \(y^{2}z-yz^{2}+z^{2}x-zx^{2}+xy\left(x-y\right)\) - step3: Simplify: \(y^{2}z-yz^{2}+z^{2}x-zx^{2}+x^{2}y-xy^{2}\) - step4: Evaluate: \(y^{2}z-y^{2}x+yx^{2}-z^{2}y+z^{2}x-zx^{2}\) - step5: Rewrite the expression: \(y^{2}z-y^{2}x-yxz+yx^{2}-z^{2}y+zyx+z^{2}x-zx^{2}\) - step6: Factor the expression: \(y\left(yz-yx-xz+x^{2}\right)-z\left(yz-yx-xz+x^{2}\right)\) - step7: Factor the expression: \(\left(y-z\right)\left(yz-yx-xz+x^{2}\right)\) - step8: Factor the expression: \(\left(y-z\right)\left(y-x\right)\left(z-x\right)\) Factor the expression \( yz(y+z)+zx(z+x)+xy(x+y)+2xyz \). Factor the expression by following steps: - step0: Factor: \(yz\left(y+z\right)+zx\left(z+x\right)+xy\left(x+y\right)+2xyz\) - step1: Simplify: \(y^{2}z+yz^{2}+zx\left(z+x\right)+xy\left(x+y\right)+2xyz\) - step2: Simplify: \(y^{2}z+yz^{2}+z^{2}x+zx^{2}+xy\left(x+y\right)+2xyz\) - step3: Simplify: \(y^{2}z+yz^{2}+z^{2}x+zx^{2}+x^{2}y+xy^{2}+2xyz\) - step4: Evaluate: \(y^{2}z+y^{2}x+2yxz+yx^{2}+z^{2}y+z^{2}x+zx^{2}\) - step5: Rewrite the expression: \(y^{2}z+y^{2}x+yxz+yx^{2}+z^{2}y+zyx+z^{2}x+zx^{2}\) - step6: Factor the expression: \(y\left(yz+yx+xz+x^{2}\right)+z\left(yz+yx+xz+x^{2}\right)\) - step7: Factor the expression: \(\left(y+z\right)\left(yz+yx+xz+x^{2}\right)\) - step8: Factor the expression: \(\left(y+z\right)\left(y+x\right)\left(z+x\right)\) The factorization of the given expressions is as follows: (i) \( yz(y-z)+zx(z-x)+xy(x-y) = (y-z)(y-x)(z-x) \) (ii) \( yz(y+z)+zx(z+x)+xy(x+y)+2xyz = (y+z)(y+x)(z+x) \)