Question

Using%C2%A0the Commutative Property,%C2%A0prove that these algebraic expressions are equivalent. In 1–2 sentences, explain your result. Expression 1:%C2%A0 y⋅3x Expression 2:%C2%A0 3xy

Answer 1

To prove that \( y \cdot 3x \) is equivalent to \( 3xy \) using the Commutative Property, we can rearrange the factors in the first expression:

1. \( y \cdot 3x = 3 \cdot y \cdot x \) (by factoring out the 3).
2. By the Commutative Property of multiplication, we can reorder the factors as \( 3 \cdot x \cdot y = 3xy \).

Thus, both expressions represent the same product. This demonstrates that the multiplication of numbers (or variables) can be rearranged without changing the outcome, confirming their equivalence.