Question

Which expressions are equivalent to x+2y+x+2 2(x+y+1) 2x+4y+y none of the above

Answer 1

Hey there!

Keep in mind that $x+2y+x+2$ is the same thing as $2x+2y+2$, 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:

$2(x+y+1)$

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:

$(2)(x) = 2x$
$(2)(y) = 2y$
$(2)(1) = 2$

$2x + 2y + 2$

This means that your first answer choice is equivalent. 

Let's take a look at your second answer choice: 

$2x+4y+y$

You can simplify this by adding together your like terms, which is the y term:

$2x+5y$

This is not equivalent, so your answer will be your first option only. 

Hope this helped you out! :-)