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Current time:0:00Total duration:4:07

Combining like terms with negative coefficients & distribution


Video transcript

I've gotten feedback that all the Chuck Noris 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(3x + 5). Well, this literally means two "3x + 5". So, this is the exact same thing as... So this is one "3x + 5", and then to that, I'm going to add another "3x + 5". This is literally what 2(3x + 5) means. Well this, is the same thing as... if we're gonna just have a look right over here, we have now two "3x". So, we can write it as 2(3x), plus we have two "5". So, plus 2(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 two "2(3x)" plus "2(5)", And I would tell you: "Yes, it is!" And, the whole reason why I'm doing this, is just to show you that it is exactly what you all already know. But with that out of the way, let's continue to simplify it. So, when you multiply the 2(3x), you get 6x. If you multiply the 2(5), you get 10. So, this simplifies to 6x + 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 7(3y - 5) - 2(10 +4y). Let's see if we can simplify this. Well, let's work on the left-hand side of the expression. The 7(3y - 5). We just have to distribute the "7". So, this is gonna be 7 times 3y, which is going to give us 21y, Or, if I had three "y" seven times, this is going to be 21y (either way you want to think about it). And then I have "7" times... We're going to be careful with the sign. This is "7" times negative 5. "7" times "-5" is "-35". So, we 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 distribute the subtraction, it would work out. But, I like to think of this as... "-2". And we're just going to distribute the "-2" times "10", and then we're going to distribute the "-2" times "4y". So, "-2" times "10" is "-20". (minus 20, right over here). And then "-2" times "4y"... "-2" times "4" is "-8", so it's going to be "-8y". So, let's write a "-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 "21y" to the "-35" or the "-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 21y, right over here. And then, from that we are subtracting 8y. So 21 of something... If I have 21 of something and I take 8 of them away, I'm left with 13 of that something. So, those are going to simplify to 13y. And then, I have "-35" minus "20". And so, that's just going to simplify to "-55". So, this whole thing simplified, using a little bit of distributive property and combining similar or like terms, we got to "13y - 55".