Combining like terms with negative coefficients & distribution

I've gotten feedback that all the Chuck Norris imagery in the last video might have been a little bit too overwhelming so for this video I've included something a little bit more soothing so let's try to simplify some more expressions and we'll see we're just applying ideas that we already knew about so let's say I want to simplify the expression 2 times 3x plus 5 well this literally means to 3x plus 5 so this is the exact same thing as so this is 1 3x plus 5 and then to that I'm gonna add another 3x plus 5 this is literally what 2 times 3x plus 5 means well this Liz the same thing as I mean if we just look at it right over here we have now 2 3 X's so we can write it as 2 times 3x plus we have two 5s plus we have 2 5 so plus 2 times 5 but you might say hey Sal isn't this just the distributive property that I know from arithmetic I've essentially just distributed the to 2 times 3 X 2 times 3x plus 2 times 5 and I would tell you yes it is and I'm the whole reason why I'm doing this is just to show you that it is exactly what you already know but with that out of the way let's continue to simplify it so when you multiply the 2 times the 3x the 2 times the 3x you get 6x you multiply the 2 times the 5 you get 10 so this simplified to 6x plus 10 now let's try something that's a little bit more involved once again really just things that you already know so let's say I had let's say that I had 7 times let's say 3y minus 5 minus 2 times 10 10 plus let's say plus 10 plus 4y let's see if we can simplify this well let's work on the left hand side of the expression the 7 times 3y minus 5 we just have to distribute the 7 so this is going to be 7 times 3y which is going to give us 21 Y or if I had three wise seven times it's going to be 21 wise you want to think about it and then I have seven times we're gonna be careful with the sign this is seven times negative five seven times negative five is negative 35 so we've simplified this part of it let's simplify the right-hand side so you might be tempted to say oh 2 times 10 and 2 times 4y and then subtract them and if you do that right and you distribute the subtraction it would work out but I like to think of this as negative 2 as negative 2 and we're gonna distribute the negative 2 times 10 and then we're going to distribute the negative or times 10 and the negative 2 times 4y so negative 2 times 10 negative 2 times the 10 is negative 20 so it's Nate minus 20 right over here and then negative 2 times 4y negative 2 times 4 is negative 8 so it's going to be negative 8y so it's quite a minus 8y right over here and are we done simplifying well no there's a little bit more that we can do we can't add the 21 Y to the negative 35 or the negative 20 because these are adding different things or subtracting different things but we do have two things that are multiplying Y we have the let me do them all in this green color you have 21 Y's right over here and then from that we are subtracting we are what we can view it as from that we are subtracting eight Y's so 21 of something might if I have 21 of something and I take eight of them away I'm left with 13 of that something so those are going to simplify to 13 Y's and then I have negative 35 is in a new color and then I have negative 35 minus 20 and so that's just going to simplify to negative 55 negative 55 so this whole thing simplified using a little bit of the distributive property and combining similar or like terms we got to 13 y minus 55