Hey there!
Keep in mind that [tex]x+2y+x+2[/tex] is the same thing as [tex]2x+2y+2[/tex], since you can add 1x and 1x together to get 2x at the beginning of your expression.
Now, take a look at your answer choices:
[tex]2(x+y+1)[/tex]
If you use the distributive property on this (which you do by multiplying 2 by each term in your trinomial), you will get the following:
[tex](2)(x) = 2x[/tex]
[tex](2)(y) = 2y[/tex]
[tex](2)(1) = 2[/tex]
[tex]2x + 2y + 2[/tex]
This means that your first answer choice is equivalent.
Let's take a look at your second answer choice:
[tex]2x+4y+y[/tex]
You can simplify this by adding together your like terms, which is the y term:
[tex]2x+5y[/tex]
This is not equivalent, so your answer will be your first option only.
Hope this helped you out! :-)
