. 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 multiplication in Expression 1:

\[ y \cdot 3x = 3 \cdot y \cdot x = 3xy. \]

Since multiplication is commutative, the order in which we multiply the numbers does not change the result. Therefore, both expressions are equivalent. This demonstrates that rearranging the factors in a multiplication operation yields the same product.