Question

Phân tich xy ( x- y ) - xz (x+ z) + yz(2x-y+z) thanh nhân tử

Answer 1

\(xy\left(x-y\right)-xz\left(x+z\right)+yz\left(2x-y+z\right)\)

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

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

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

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

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

Answer 2

Ta có :

xy(x−y)−xz(x+z)+yz(2x−y+z)

=xy(x−y)−xz(x+z)+yz(x−y+x+z)

=xy(x−y)−xz(x+z)+yz(x−y)+yz(x+z)

=(x−y)(xy+yz)−(xz−yz)(x+z)

=y(x−y)(x+z)−z(x−y)(x+z)

=(y−z)(x−y)(x+z)

P/s tham khảo nha