Question

phân tích đa thức sau thành nhân tử :

xy(x-y) - xz(x+z) +yz(2x+z-y)

Answer 1

\(\text{xy(x-y)-xz(x+z)+yz(2x+z-y)}\\ =xy\left(x-y\right)-x^2z-xz^2+2xyz+yz^2-y^2z\\ =xy\left(x-y\right)-z\left(x^2-2xy+y^2\right)-z^2\left(x-y\right)\\ =\left(x-y\right)\left(xy-zx+zy-z^2\right)\\ =\left(x-y\right)\left(y-z\right)\left(x+z\right)\)