Using the Commutative Property, prove that these algebraic expressions are equivalent. In 1–2 sentences, explain your result.

Question

Expression 1: y⋅3x


Expression 2: 3xy

Answer 1

To prove the equivalence of the expressions \( y \cdot 3x \) and \( 3xy \) using the Commutative Property, we can rearrange the terms:

1. Starting with Expression 1: \( y \cdot 3x \)
2. By the Commutative Property, we can rearrange it as \( 3 \cdot (y \cdot x) \).
3. We can further apply the Commutative Property to get \( 3xy \).

Thus, \( y \cdot 3x = 3xy \).

This shows that both expressions are equivalent because multiplication is commutative, allowing us to rearrange the factors without changing the product.