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Equivalent expressions

In this math lesson, we learn how to find equivalent expressions by combining like terms and factoring. We start with an expression like x + 2 - y + x + 2 and simplify it by adding the x terms and factoring out common factors. This helps us compare expressions and solve problems more easily.

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Video 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".