About this video
The video finds which expressions are equivalent to x + 2y + x + 2. It combines the two x's to get 2x + 2y + 2, rules out 2x + 4y + 4, and then factors out a 2 to show that 2(x + y + 1) is equivalent.
You'll be able to
- combine like terms to rewrite an expression.
- factor out a common factor to find an equivalent expression.
- decide whether two expressions are equivalent.
Key words
- equivalent expressions
- Expressions that always have the same value, whatever numbers the variables stand for.
- factor out
- Take a common factor from every term and write it outside brackets, like 2x + 2 = 2(x + 1).
Transcript
- 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".
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