Topic A: Use properties of operations to generate equivalent expressions
- Let's get some practice identifying equivalent expressions. So I have an expression written here in yellow and then I have two more written in this light green color. And I want you to pause this video and see if you can figure out which of these expressions, and it's possible that neither of them are, which of these are equivalent to the one in yellow. So I'm assuming you've had a go at it. So the way I like to tackle it is just to simplify all of them as much as possible. So this one up here is clearly not that simplified. So let's distribute this two. So if I distribute the two, what does it become? This is equal to two times negative six-C, is negative 12-C. Two times positive three is positive six. And then we have plus four-C, plus four-C. And then we can simplify it further cause I have both of these terms that involve C. I have negative 12-C plus four-C. So what's that going to be? Negative 12 of something plus four of something is going to be negative eight of that something. So this is going to be equal to negative eight-C. So these two blue terms when I add them, I'm going to get negative eight-C. And then finally plus six. Plus six. Now just doing that that's exactly what this first green expression is. So this one is definitely, this one is definitely going to be equivalent. Now what about this one down here? Well to figure that out let's simplify it. So let's distribute the three. Three times negative four-C is negative 12-C. Three times positive two is positive six. So plus six and then we have the plus four-C over there. It's lookin' good. And then we can add the terms that involve C. Negative 12-C and four-C, you add those together, you're gonna get negative eight-C. Negative eight-C plus six. Plus six, which is exactly what these other ones are. So all of these, all of these expressions, are actually equivalent. This one, that one, and that one. Let's do another example. And just like the last time pause the video and see which of these two expressions, it could be both of them or it could be none of them, or it could be one of them. Which of them, if any, are equivalent to this yellow expression? Alright let's do it together. And like before let's just simplify it. So the first thing my brain wants to do is let's take the terms involving N and add those together. So negative six of something, in this case N, plus four of that something, in that case N. So negative six-N plus four-N that's gonna leave you with negative two of that something. You add the coefficients. Negative six plus four is negative two Ns. So we have negative two-N, and then plus negative 12, that's the same thing as just minus 12. So minus, minus 12. So I simplified our original expression. Let's see these ones, these down here. So if I distribute the four, if I distribute the four I get four times N is four-N. And then four times negative three is minus 12. And then we are going to subtract six-N. So minus six-N. So what does this give us? We get, let me get another color here. So we have four-N, I'm adding all the terms with N, minus six-N, that's gonna give us negative two-N. And then we have the minus 12. And then we have the minus 12. So this expression when I simplify it got me the exact same place as the first expression. So these two, these two are equivalent. This is equivalent to that. Now let's check this one out. So two, let me just distribute, let me just distribute the two. Two times two-N is four-N. And then two times negative six is negative 12. So this simplified to four-N minus 12 which is clearly different than negative two-N minus 12. So this one, this one, is not the same as the other two.