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# Equivalent expressions: negative numbers & distribution

## Thuyết minh video

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 had a go at it so the way I like to tackle these 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 to so if I distribute the two what does it become this is equal to two times negative six C is negative twelve C two times positive three is positive six and then we have plus 4 c plus four C and then we can simplify it further because I have both of these terms that involve C I have negative twelve C plus four C so what's that going to be negative twelve 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 3 3 times negative 4 C is negative 12 C 3 times positive 2 is positive 6 so plus 6 and we have the plus 4 C over there it's looking good so and then we can add the terms that involve C negative 12 C + 4 C you add those together you're going to get negative 8 C negative 8 C plus 6 plus 6 which is I did 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 could be none of them or could be one of them which which of them if any our 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 6 of something in this case n plus 4 of that something in that case and so negative 6 n plus 4n that's going to leave you with negative 2 of that something you add the coefficients negative 6 plus 4 is negative 2 ends so we have negative 2n and then plus negative 12 that's the same thing it's just minus 12 so minus minus 12 so I simplified our original expression let's see these ones these D's down here so if I distribute the 4 if I distribute the 4 I get 4 times n is 4 n and then 4 times negative 3 is minus 12 and then we are going to subtract 6 n so minus 6 n so what is this give us we get we get another color here so we have 4 n I'm adding all the terms with n minus 6 n that's going to give us negative 2n 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 to let me just distribute let me just distribute the 2 2 times 2 n is 4 n and then 2 times negative 6 is negative 12 so this simplifies to 4 n minus 12 which is clearly different than negative 2 n minus 12 so this one this one is not the same as the other two