Khi phân tích đa thức \(xy\left(x+y\right)+yz\left(y+z\right)+zx\left(z+x\right)+2xyz\) thành nhân tử, ta có kết quả là
\(\left(x+y\right)\left(y+z\right)\left(z+x\right)\).\(\left(x+y+z\right)\left(x+y-z\right)\).\(\left(x^2+y^2+x^2\right)\left(x+y+z\right)\).\(\left(x-y\right)\left(y-z\right)\left(z-x\right)\).Hướng dẫn giải:\(xy\left(x+y\right)+yz\left(y+z\right)+zx\left(z+x\right)+2xyz\)
\(=xy\left(x+y\right)+xyz+yz\left(y+z\right)+xyz+zx\left(z+x\right)\)
\(=xy\left(x+y+z\right)+yz\left(z+y+z\right)+zx\left(z+x\right)\)
\(=y\left(x+y+z\right)\left(z+x\right)+zx\left(z+x\right)\)
\(=\left(z+x\right)\left[y\left(x+y+z\right)+zx\right]\)
\(=\left(z+x\right)\left(yx+y^2+yz+zx\right)\)
\(=\left(z+x\right)\left[y\left(x+y\right)+z\left(y+x\right)\right]\)
\(=\left(z+x\right)\left(y+z\right)\left(x+y\right)\)
\(=\left(x+y\right)\left(y+z\right)\left(z+x\right)\).