Question

`2 + a + b = a + 2 + b` is an example of which algebraic property?

Answer 1

It is an example of at least two algebraic properties:

Commutativity and associativity.

Explanation:

Addition is:

Commutative: `A+B = B+A`

Associative: `(A+B)+C = A+(B+C)`

The example `2+a+b = a+2+b` uses commutativity to get `2+a = a + 2` and hence `2+a+b = a+2+b`.

The example also uses associativity to even write `2 + a + b`. Without associativity, we would need to write: `(2+a)+b` or `2+(a+b)`, etc.

The example also expresses equality, which might also be counted as an algebraic property, but is often just assumed.