How to simplify an expression by combining like terms and the distributive property | Khan Academy
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How to simplify an expression by combining like terms and the distributive property | Khan Academy

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”.

100 thoughts on “How to simplify an expression by combining like terms and the distributive property | Khan Academy

  1. Thank you! These videos are greatly helping me to get through college algebra. I really appreciate your time for making these videos. I'm sure you have helped many. Keep up the great work 🙂

  2. I am estatic. I struggled for 2 hours understanding this for class and after watching this video I just got 3 questions back to back right. THANK YOU

  3. Okay my work question are this
    1: x+x+x+1+x squared+x squared+x squared+1+1+1+1
    How do I simplify this expression HEEEEEEEEEEEEEEEEEEELP

  4. But what about
    Its the longer, multi step problems that get me.
    Using distribution and combining like terms to simplify: Univariate

  5. Can you put Arnold schwarzenegger for your video. Cuz I wanna say hasta la vista baby to my math by terminating it.

  6. What is 3(2z – 7) = 5z + 17 + z

    6z – 21 = 5z + 17 + z
    6z – 21 = 6z + 17
    – 6z -6z
    -21 = 17
    +21 = +21
    0= 38. I know it's wrong! I need help what's the answer how do you do this one? Answer please I beg!

  7. Thank you, I found yhis helpful but please, what does the macho idiocy of Chuck Norris have to do with the beauty of math to begin with?

  8. I’m super confused…..this is what I have to do: 4(4 – 4m) +8(1 + 7m) How the hell am I supposed to do that? High school sucks

  9. I have trouble in class bc of a girl I like so it’s hard for me to focus and I have a test tomorrow so thank you for the help 🙏

  10. I'm stressing out. Math is so confusing. I have two assignments due tomorrow night and I forgot we had a unit test yesterday which I did okay in thank Jesus but its just so confusing. Ugh. And I want to be good at physics. :/

  11. It seems like you mixed up your wording while explaining this expression, which made simplifying it confusing. When you originally wrote out 7(3y-5), you explained it as "7 times 3y minus 5". But, when you went to simplify it, you explained it as "7 times 3y times -5". Those are two completely different things with different simplifications.

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