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

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. Khan Academy is saving my grades so thanks :')

  2. Thank you for doing this. You're helping so much! I have a test tomorrow and this will help me

  3. I'm not trying to be rude or anything but is it bad that I skipped over some courses because I wanted to learn calculus right away?

  4. What do i do when it says 4(3x) x=-3 I need help please help

  5. You suck You make no SENCE

  6. Cdlc is here

  7. Ayyyy Laputeite!

  8. he needs some milk

  9. Thanks
    This really helped a lot

  10. ITS SOO FLUFFFYYYY!!!!

  11. what's with Chuck Norris

  12. Thanks I need this for my math class

  13. want the left one in the beginning MINUS 5???? I'm really confused right now.

  14. ^_^

  15. Thx 😭

  16. Sal explains way better than my teacher ^^!

  17. 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 🙂

  18. this is still very hard for me

  19. your name is Sal?

  20. this video is so boring its amazing that I am still alive.

  21. popping the arrows

  22. 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

  23. What? I loved the Chuck Norrises!!

  24. why did he add together the 20 and 35??

  25. i'm in third grade and i have to do harder problems
    but this helped me

  26. Khan should just go ahead and start an online home schooling service

  27. what about 6y-y or -8a-2a?

  28. anyone know how to do this with a number that has exponents?

  29. Wow, young America "stop being so overwhelmed", its annoying thank you Sal your videos are incredibly helpful.

  30. Thank you so much my math teacher just doesn't teach me anything he tells me to teach "yourself"

  31. wait is this simplifying polynomials and also distributive property?

  32. Con Academy

  33. 1,000th like :3. Thanks for helping me pass my math quiz 😀

  34. They're asking me to simplify (12 + m ) + 4
    Totally confused, this video hasn't solved my problem. 🙁

  35. I'm 13 jus' checking up after the summer

  36. 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

  37. Lol! Today in math we watched your "Chuck Norris" video and everybody was laughing so hard!! p.s. helpful video.

  38. Be my math teacher

  39. HE PUT "NOT CHUCK NORRIS" IM MUERTO HAHA!!!!!

  40. I don’t learn anything from my maths teacher he sucks so I come here instead. Thanks a lot Khan Academy 🙏

  41. to much not chuck noreses

  42. Chuck Norris' got a little overwhelming! Lmao. 😀

  43. Its better than my teacher but I still dont understand

  44. Can you do Birds or foxes/wolves?

  45. thank you Sal your academy is excellent

  46. omg i was so confused. thx so much sal u just saved me

  47. hi

  48. Your way more helpful than my teacher

  49. I still don't get it.

  50. screw math taechers

  51. Thank u u get everything now

  52. So simple and great. Thanks Sal!

  53. #very helpful

  54. do you guys have to watch this for school

  55. But what about
    3(3x-6)+5(4x-2)?
    Its the longer, multi step problems that get me.
    Using distribution and combining like terms to simplify: Univariate

  56. it's still confusing as hell. this is why i dropped math/Algebra, i could not get past this point.

  57. My brain has popped

  58. you can never have too much Chuck Norris

  59. I've watched this video 5 times and still don't understand.

  60. Thanks

  61. I like chuck Norris

  62. I liked the Chuck Norris approach… I mean if you think about it he's a kind of reliable character.

  63. What is 16-4(n-4). Help me solve please

  64. Started High-school this year, I have trouble with addition and subtraction HAHAHA

  65. I was so ready for math then I heard him say chuck Norris and I couldn’t be serious after that

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

  67. You move to fast

  68. This is a great video… I watched it for my 7th grade Pre-Algebra test for studying! very helpful

  69. thanks i acing my tests

  70. What is 3(2z – 7) = 5z + 17 + z

    I NEED HALP
    HERE'S MAH WORK…
    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!

  71. You explain it way easier than any of my math teacher so thank god for you :O

  72. this just saved me and my math homework

  73. THANK YOU I was confused when I did problems in class like the last one you solved THANKS

  74. AMAZING

  75. noice 2018

  76. 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?

  77. This is kinda hard:p

  78. I love how dated this video is with that Chuck Norris reference.

  79. you pretty much saved my life in pre algebra

  80. this dude i wish he was my math teacher lol

  81. Mental abuse to humans =math

  82. 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

  83. That's smart

  84. My man needs a sprite cranberry

  85. I always come to khan academy when I don’t listen in class🤣

  86. 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 🙏

  87. Me is dumb not helping

  88. Polar Bear+100000000000% CHUCK NORRIS!!

  89. God bless you and your family my dear friend

  90. My mature side: This is quality help with math. Thank you!

    my not mature side lol: meth hue

  91. I still don't understand.

  92. 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. :/

  93. Ok, This is epic

  94. What a god lmao, any 2019 viewers?

  95. You seemed angry

  96. 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.

  97. Thanks so much 😭♥️

  98. hahah lol, give a cookie

  99. why can't we all have a teacher like Sal

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