Final answer:
Two equivalent expressions for 2(2y-4) are 4y - 8 and the original expression 2(2y-4) itself, obtained using the distributive property of multiplication over addition.
Step-by-step explanation:
To write two equivalent expressions for 2(2y-4), we can use the distributive property of multiplication over addition. The distributive property allows us to multiply each term inside the parentheses by 2, which gives us:
2 * 2y - 2 * 4 = 4y - 8
This is the first equivalent expression. The second equivalent expression can be obtained by factoring out a common factor from the terms if possible. In this case, since there aren't any common factors other than 1, we are left with the original expression and the one we've found using distribution.
Therefore, the two equivalent expressions are 2(2y-4) and 4y - 8.
If we were to try and find another equivalent expression, we would have to look for a term that can be factored out or apply another property of operations, but in this case, there is no simpler way to write the expression.