To be factored into the product of three factors:

$$
\left(x^{2}+x y+y^{2}\right)^{2}-\left(x^{2} y^{2}+y^{2} z^{2}+z^{2} x^{2}\right)
$$
The difference of squares of two terms,

$$
\begin{aligned}
\left(x^{2}+x y+y^{2}\right)^{2}-x^{2} y^{2} & =\left(x^{2}+x y+y^{2}+x y\right)\left(x^{2}+x y+y^{2}-x y\right)= \\
& =(x+y)^{2}\left(x^{2}+y^{2}\right)
\end{aligned}
$$

According to the given expression,

$$
\begin{gathered}
\left.(x+y)^{2}\left(x^{2}+y^{2}\right)-z^{2}\left(x^{2}+y^{2}\right)=\left(x^{2}+y^{2}\right)\left[(x+y)^{2}-z^{2}\right)\right]= \\
=\left(x^{2}+y^{2}\right)(x+y+z)(x+y-z)
\end{gathered}
$$

it can be written in the form.