29.52 $x^{2} y-y^{2} z+z^{2} x-x^{2} z+y^{2} x+z^{2} y-2 x y z$ The result of factorization is
(A) $(y-z) \cdot(x+y) \cdot(x-z)$.
(B) $(y-z) \cdot(x-y) \cdot(x+z)$.
(C) $(y+z) \cdot(x-y) \cdot(x+z)$.
(D) $(y+z) \cdot(x+y) \cdot(x-z)$.
(Shanghai Junior High School Mathematics Competition, 1985)
[Solution]
$$
\begin{aligned}
\text { Original expression } & =\left(x^{2} y-x^{2} z\right)+\left(z^{2} y-y^{2} z\right)+\left(y^{2} x-2 x y z+z^{2} x\right) \\
& =x^{2}(y-z)+y z(z-y)+x(y-z)^{2} \\
& =(y-z)\left[x^{2}-y z+x(y-z)\right] \\
& =(y-z)\left(x^{2}-y z+x y-x z\right) \\
& =(y-z)[x(x-z)+y(x-z)] \\
& =(y-z)(x-z)(x+y) .
\end{aligned}
$$

Therefore, the correct choice is (A).