How to find equivalent expressions by combining like terms and using the distributive property

- Which expressions are equivalent

to x plus two-y plus x plus two?

Select all that apply. Alright.

Let's see if I can manipulate
this thing a little bit.

Let me just rewrite it so I have x plus...

x plus two-y plus x plus two.

So, the first thing that jumps out at me,

before I even look at these choices,

here I have an x over here,
I have an x over there.

Well, if I have one x, and
then I can add it to another x

that would be two-x so
I could rewrite this...

let me do this in a different color.

I could rewrite this x and this x,

if I add them together
that's going to be two-x.

So, this is...actually, I
don't want to skip any steps.

So, that's x plus x plus two-y...

now I'm just switching
the order...plus two.

And then these two x's right over here,

I can just rewrite that as two-x.

So, I have two-x plus two-y...

plus two-y plus two.

Now, let's see, out of all my choices...

so, this one,

this is two-x plus four-y plus four.

So, that's not right, I have
two-x plus two-y plus 2,

so I can rule this one out.

Now, this one's interesting, it looks like

they have factored out a two.

Let's see if we factor out
a two here, what happens?

So, we do see that two
is a factor of that term,

it's a factor of that term,
and it's a factor of that term.

So, let's see if we can factor it out.

So, this is going to be two times x,

I'll do the x in that same
magenta color, two times x plus,

we have just a y left when
you factor out the two.

And then if you factor out a two here,

you're just going to have a one left.

So, two times x plus y plus one.

Which is exactly what they have over here.

And since I was able to find a choice,

I will not pick "None of the above".