Question

Choose 2 axioms that allows 22 + (m + 8) to be written as m + 30
commutative - addition
distributive
associative - multiplication
symmetric
commutative - multiplication
associative - addition
identity - addition

Answer 1

commutative for addition
\[22+(m+8)=(m+8)+22\] then associative
\[(m+8)+22=m+(8+22)\]
\[=m+30\]

Answer 2

don't even need that, just do the associative property of addition and you're done.
\[22 + (m + 8) = m + (22+8)\]

Answer 3

unless you need to choose two of them that could do it, then satellite's right.

Answer 4

not to get picky but without the commutative law you cannot get from \[22+(m+8)\] to
\[m+(22+8)\]