simplify produces wrong answer with non-commuting symbols

[jtmacair]

I'm not sure why #25572 was closed. A misreading of the expressions maybe? Let me try one more time.

To see the problem, please look at the term that contains the non-commuting symbols A and B in the original expression and compare it with the corresponding term in the output. Simplify has incorrectly reversed the order from BA to AB within the same term. (The other terms are just part of the context in which the problem occurs.)

from sympy import *
x = symbols('x')
A, B = symbols('A B', commutative=False)
expr = 2*cos(x)*sin(x)*B*A + cos(x)**2
print(expr.simplify())

Output

sin(2*x)*A*B + cos(2*x)/2 + 1/2

[sylee957]

I confirm that the issue is valid
having the cos(x)**2 triggers the changes of the wrong result

expr = 2*cos(x)*sin(x)*B*A
print(expr.simplify())

sin(2*x)*B*A