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 that the expressions \( y \cdot 3x \) and \( 3xy \) are equivalent using the Commutative Property, we can rearrange the terms in Expression 1. By applying the Commutative Property, we have:

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

Since both expressions simplify to the same form, \( 3xy \), they are equivalent. This result demonstrates that the order of multiplication does not affect the final product, showcasing the Commutative Property of multiplication.

Answer 2

Use the Associative Property to demonstrate that Expression 1 is equivalent to Expression 2. Expression 1: 22r−13 Expression 2: 19r+(3r−2)−11