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
Expression 1: y∙3x
Expression 2: 3xy
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GPT-4o mini
To prove the equivalence of the expressions \( y \cdot 3x \) and \( 3xy \) using the Commutative Property, we can rearrange the multiplication in Expression 1:
\[
y \cdot 3x = 3 \cdot y \cdot x = 3xy.
\]
Since multiplication is commutative, the order in which we multiply the numbers does not change the result. Therefore, both expressions are equivalent. This demonstrates that rearranging the factors in a multiplication operation yields the same product.
\[
y \cdot 3x = 3 \cdot y \cdot x = 3xy.
\]
Since multiplication is commutative, the order in which we multiply the numbers does not change the result. Therefore, both expressions are equivalent. This demonstrates that rearranging the factors in a multiplication operation yields the same product.
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