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! :-)