Xin phép được sửa đề :3
\(x\left(y^2+z^2\right)+y\left(z^2+x^2\right)+z\left(x^2+y^2\right)+2xyz\)
\(=xy^2+xz^2+yz^2+yx^2+zx^2+zy^2+xyz+xyz\)
\(=\left(xy^2+yx^2+xyz\right)+\left(yz^2+zy^2+xyz\right)+\left(xz^2+zx^2\right)\)
\(=\left[xy\left(x+y+z\right)+yz\left(x+y+z\right)\right]+xz\left(x+z\right)\)
\(=\left(x+y+z\right)\left(xy+yz\right)+xz\left(x+z\right)\)
\(=y\left(x+z\right)\left(x+y+z\right)+xz\left(x+z\right)\)
\(=\left(x+z\right)\left[y\left(x+y+z\right)+xz\right]\)
\(=\left(x+z\right)\left(xy+yz+xz+y^2\right)\)
\(=\left(x+z\right)\left[y\left(x+y\right)+z\left(x+y\right)\right]\)
\(=\left(x+z\right)\left(x+y\right)\left(y+z\right)\)
