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 : A(B + C) + B(CA)(A+B)C


So, we know that

A(B+C) = AB + AC
(A+B)C= AC + BC
B(CA) = (BC)A

So...how can i simplify the expression?

AB+AC + (BC)A*(AC+BC) ?? and now?