Question

Using the Commutative Property, prove that these algebraic expressions are equivalent. In 1–2 sentences, explain your result. y times 3x 3xy
step by step

Answer 1

To prove that the expressions \( y \times 3x \) and \( 3xy \) are equivalent using the Commutative Property, we follow these steps:

1. Start with the expression \( y \times 3x \).
2. By the Commutative Property of multiplication, we can rearrange the factors: \( y \times 3x = 3 \times y \times x \).
3. By further applying the Commutative Property, we can write this as \( 3 \times x \times y = 3xy \).

Thus, \( y \times 3x = 3xy \).

The equivalence of the two expressions is established through the Commutative Property, which allows us to rearrange the order of multiplication without changing the product.