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

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

GPT-4o mini · Answer

To prove that $ y \cdot 3x $ is equivalent to $ 3xy $ using the Commutative Property, we can rearrange the terms in Expression 1: $$ y \cdot 3x = 3 \cdot y \cdot x = 3xy. $$ Thus, both expressions are equivalent because we can change the order of multiplication without affecting the result. The Commutative Property shows that the order of factors does not change the product.