Question

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

Expression 1: y⋅3x

Expression 2: 3xy

Answer 1

To prove the equivalence of the expressions using the Commutative Property of multiplication, we can rearrange the factors in Expression 1: \( y \cdot 3x = 3 \cdot y \cdot x = 3xy \). Thus, both expressions are equivalent since they represent the same product of the same three variables multiplied together.

As a result, this shows that the order of multiplication does not affect the final product, confirming that \( y \cdot 3x \) and \( 3xy \) are indeed equivalent expressions.