Final answer:
The expression equivalent to 3 (x+y) is 3x + 3y using the distributive property, and by applying the commutative property of addition, it can also be written as 3y + 3x, although this does not change the meaning or value of the expression.
Step-by-step explanation:
To write an expression equivalent to 3 (x+y) using the distributive property of multiplication over addition, you multiply each term inside the parentheses by 3. So, the expression becomes 3x + 3y.
Using the commutative property of addition, which states that A+B=B+A, you can rearrange the terms in the expression 3x + 3y to 3y + 3x. However, since multiplication does not fundamentally change when rearranging the terms being added, this application of the commutative property does not alter the expression significantly, it merely changes the order of the terms.
Thus, the expression equivalent to 3 (x+y) using the distributive property is 3x + 3y, and using the commutative property, while it remains essentially the same, can be written as 3y + 3x.