Question

[Vy Hoàng]

Phân tích thành nhân tử :

y(x-2z)^2+8xyz+x(y-2z)^2-2z(x+y)^2

Answer 1

[Ngô Tùng Lâm]

y(x−2z)²+8xyz+x(y−2z)²−2z(x+y)²
=y(x²−4xz+4z²)+8xyz+x(y²−4yz+4z²)−2z(x²+y²+2xy)

=(yx²+xy²)+(4yz²+4xz²)−(2zx²+2zy²+4xyz)

=xy(x+y)+4z²(x+y)−2z(x²+y²+2xy)

=xy(x+y)+4z²(x+y)−2z(x+y)²

=(x+y)(xy+4z²−2xz−2yz)

=(x+y)[y(x−2z)−2z(x−2z)]

=(x+y)(y−2z)(x−2z)