Answer:
The property that best explains the equivalence of the two expressions is the distributive property of multiplication over addition.
The distributive property states that for any real numbers a, b, and c, the expression a(b + c) is equal to ab + ac.
In the given expressions, we have 3(z + 8) and 3z + 3(8). By applying the distributive property, we can expand the first expression as follows:
3(z + 8) = 3z + 3(8)
The distributive property allows us to distribute the 3 to both terms inside the parentheses, resulting in the equivalent expression 3z + 24.
Therefore, the distributive property is the property that explains the equivalence of the two expressions.