a×bb×a

The mathematical expression "a×bb×a" is an example of a string of symbols that, without further context or definition, can be interpreted in several ways. The most common interpretation, particularly in algebraic notation, is a multiplication of four variables: a, b, b, and a. In this context, the expression can be simplified due to the commutative property of multiplication. This property allows the order of factors in a multiplication to be changed without altering the result. Therefore, a×bb×a is equivalent to a×a×b×b. This can be further expressed using exponents as a^2 × b^2, or (a×b)^2.

Alternatively, if "bb" is intended to represent a single entity or a specific notation, the interpretation changes. For instance, in some programming contexts, "bb" might be a variable name, leading to the expression a × variable_bb × a. Without a clear definition of what "bb" signifies within the "a×bb×a" construct, it remains ambiguous. In pure mathematics, the standard interpretation relies on the commutative and associative properties of multiplication, leading to the simplified form (ab)^2. The absence of explicit operators between "a" and "bb" and between "bb" and "a" in some notations, like "abb a", would conventionally imply multiplication as well, but the explicit "×" symbols in "a×bb×a" leave little room for interpretation beyond multiplication.