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 · Accepted Answer

To prove that the expressions $ y \cdot 3x $ and $ 3xy $ are equivalent using the Commutative Property, we can rearrange the factors in Expression 1: $$ y \cdot 3x = 3 \cdot y \cdot x = 3xy $$ Thus, both expressions simplify to $ 3xy $, demonstrating their equivalence. This result shows that multiplication is commutative, allowing us to rearrange the order of factors without changing the product.