I am going to try to traduce the problem:

A. B and C are matrix(s) quadratics with the same order.
Simplify the following expression

Expression : $\displaystyle A(B + C) + B(CA)(A+B)C$


So, we know that

$\displaystyle A(B+C) = AB + AC$
$\displaystyle (A+B)C= AC + BC$
$\displaystyle B(CA) = (BC)A$

So...how can i simplify the expression?

$\displaystyle AB+AC + (BC)A*(AC+BC)$ ?? and now?