Thanks everyone for the interest and interaction. I made a solution based on mmcdara 4236 idea.

I will repeat the question in another way.

I have    e=+-1    ( e is a constant number equal to plus or minus one) 

that is,   e^2=1,   e^3=e,   e^4=1,   e^5=e .... e^{2n}=1  and  e^{2n+1}=e.  .... (1)

How do I calculate (With Maple) the power of any expression written in terms of e taking into account the formulas (1)?

For example:
1)  I want the expression E= ( e + 1)^3 after the calculation in Maple to be  e^3 + 3e^2+3e + 1 = e+3+3e+1=4e+4

2)  I want the expression E= ( e + 1)^4 after the calculation in Maple to be 

                                           e^4 + 4e^3+6e^2 +4e+ 1 =1+4e+6+4e+1= 8e+8,

and so on.

Thank you but that is not what I want.

putting  X=+-1    ( plus or minus 1)

So,  X^2=1,   X^3=X,   X^4=1,   X^5=X

....X^{2n}=1 and X^{2n+1}=X

Therefore, how can Maple calculate as follows:

X^3  Y + X^2  Z + X = X Y + Z + X  ???

I think the question is now understood