Answer: Yes, they are equivalent expressions.
Explanation:
To show that two expressions are equivalent, we need to simplify both expressions and show that they are equal.
Starting with the first expression:
2x + 8
We can see that there are no common factors we can factor out, so this expression is already simplified.
Now let's simplify the second expression:
2(x + 4) + 4
Using the distributive property, we can simplify this as:
2x + 8 + 4
Simplifying further, we get:
2x + 12
Now we can see that the two expressions are equivalent since 2x + 8 and 2x + 12 represent the same value for any value of x. Therefore, we know that the two expressions are equivalent.