41*. Factor the polynomial with real coefficients:

$$
x\left(y^{2}-z^{2}\right)+y\left(z^{2}-x^{2}\right)+z\left(x^{2}-y^{2}\right)
$$
$\triangle$ From this sum, we can factor out the term $y-z$. We will have:

$$
\begin{aligned}
& x\left(y^{2}-z^{2}\right)+y\left(z^{2}-x^{2}\right)+z\left(x^{2}-y^{2}\right)=x(y+z)(y-z)+y z^{2}-y x^{2}+z x^{2}-z y^{2}= \\
& =(y-z)(x y+x z)-y z(y-z)-x^{2}(y-z)=(y-z)\left(x y+x z-y z-x^{2}\right)= \\
& =(y-z)(x(z-x)-y(z-x))=(y-z)(z-x)(x-y) \\
& \quad \text { Answer: }(x-y)(y-z)(z-x) .
\end{aligned}
$$