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

Question

Expression 1:
z ⋅ 4x
Expression 2: 4xz

Answer 1

To prove that the expressions \( z \cdot 4x \) and \( 4xz \) are equivalent using the Commutative Property, we can rearrange the factors in the first expression:

1. By the Commutative Property of multiplication, we can rearrange the terms in \( z \cdot 4x \) to get \( 4 \cdot z \cdot x = 4xz \).

Since both expressions simplify to \( 4xz \), they are equivalent. This demonstrates that the order of multiplication does not affect the product, highlighting the Commutative Property's fundamental role in algebra.