Question

phân tích đa thức thành nhân tử :(x-y)^3+(y-2)^3+(2-x)^3      x^2*y*z*(y-z)+y^2*z^2*(z-y)          x^3+y^3+z^3-3*x*y*z

Answer 1

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

\(=\left(x+y\right)^3-3xy\left(x+y\right)+z^3-3xyz\)

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

\(=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-zx\right)\)

Answer 2

Bài 3) 

Ta có :

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

\(\Rightarrow\left(x+y\right)^3-3xy\left(x+y\right)+z^3-3xyz\)

\(\Rightarrow\left(x+y+z\right)\left[\left(x+y^2\right)-\left(x+y\right)z+z^2\right]-3xy\left(x+y+z\right)\)

\(\Rightarrow\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-zx\right)\)

P/s tham khảo nha

hok tốt