1. Factorize the expression into prime factors

$$
b c(b+c)+c a(c-a)-a b(a+b)
$$
Solution. We have

$$
\begin{aligned}
b c(b+c)+c a(c-a)-a b(a+b) & =b c(b+c)+a\left(c^{2}-a c-a b-b^{2}\right) \\
& =b c(b+c)+a[(c-b)(c+b)-a(c+b)] \\
& =b c(b+c)+a(b+c)(c-b-a) \\
& =(b+c)\left(b c+a c-a b-a^{2}\right) \\
& =(b+c)[c(b+a)-(a(b+a)] \\
& =(a+b)(b+c)(c-a) .
\end{aligned}
$$