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 that \( y \cdot 3x \) is equivalent to \( 3xy \) using the Commutative Property, we can rearrange the factors in Expression 1:

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

Thus, both expressions represent the same product of the numbers and variables. This shows that the expressions are equivalent due to the Commutative Property of multiplication, which states that the order of factors can be changed without affecting the product.