Question

phân tích đa thức thành nhân tử;\(A=x^3+y^3+z^3-3xyz\)

Answer 1

\(A=x^3+y^3+z^3-3xyz\)

\(A=\left(x+y+z\right)\left[\left(x+y\right)^2-\left(x+y\right)z+z^2\right]-3xy\left(x+y+z\right)\)\(A=\left(x+y+z\right)\left(x^2+2xy+y^2-xz-yz+z^2-3xy\right)\)\(A=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-xz\right)\)

Answer 2

\(pt\Leftrightarrow A=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-xz\right)\)

Answer 3

A=\(x^3+y^3+z^3-3xyz=\left(x+y\right)^2-3xy\left(x+y\right)+z^3-3xyz=\left(x+y+z\right)\left[\left(x+y\right)^2+\left(x+y\right)z+z^2\right]-3xy\left(x+y+z\right)=\left(z+y+z\right)\left[x^2+2xy+y^2+xz+yz+z^2+-3xy\right]\)