Question

Using the commutative property, prove that these algebraic expressions are equivalent. In 1-2 sentences, explain your result.
Expression one: y • 3x
Expression two: 3xy

Answer 1

To show that the expressions \( y \cdot 3x \) and \( 3xy \) are equivalent using the commutative property, we can reorganize the terms in the first expression: \( y \cdot 3x = (y \cdot 3) \cdot x = 3 \cdot y \cdot x = 3xy \). Thus, both expressions represent the same quantity, confirming their equivalence. The result indicates that the order of multiplication does not affect the outcome in algebraic expressions.