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

Oct 25, 2015

It is an example of at least two algebraic properties:

Commutativity and associativity.

Explanation:

Commutative: $A + B = B + A$
Associative: $\left(A + B\right) + C = A + \left(B + C\right)$
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: $\left(2 + a\right) + b$ or $2 + \left(a + b\right)$, etc.