I want to clarify this and post this question again.

Expanding Expressions
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Given an expression of variables (`[a-z]`), identities (`1, 0, T`), operators (`*, +, &`) and parenthesizes, expand it using the following axioms:

    a * b != b * a
    a * b * c = (a * b) * c = a * (b * c)
    a + b = b + a
    a + b + c = (a + b) + c = a + (b + c)
    a * (b + c) = a * b + a * c
    a & b = b & a
    a & (b + c) = a & b + a & c
    a * 1 = a
    a * 0 = 0
    1 * a = a * 1
    a + 0 = a
    T & a = a
    a & a = a