- 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".