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Factoring with the distributive property

Sal shows how to factor the expression 4x+18 into the expression 2(2x+9). Created by Sal Khan.

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  • sneak peak green style avatar for user Bookworm88
    how does this help me in real life?
    (37 votes)
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  • purple pi teal style avatar for user marisa parrot
    Can someone tell me what I did wrong here with this equation? The equation is -2(-7k+4)+9=-13 I distributed -2 with -7k and 4 so when I got that I got 14k and -8 so then you put it back in the equation as 14k + -8 +9=-13 right? But then I got stuck with the -8 and 9 I can't figure it out and I have a test on it tomorrow. I need help! I need help with what to do from the step with the -8 and 9. If anyone can figure it out today that would be amazing!! I'm BEGGING YOU
    (9 votes)
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  • blobby green style avatar for user sowersc27
    can you explain distributive property
    (3 votes)
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    • mr pink green style avatar for user David Severin
      Imagine you have to pass out (distribute) papers to everyone in your class. There are 27 students in your class. The first day, you pass out 1 piece of paper to each, so you have 1(27)=27 pieces of paper. The second day, you distribute 2 pieces of to each student 2(27)=54 pieces to distribute. The third day, each student gets 3 papers, so you distribute 3(27)=81. So you have to multiply the number on the outside times the number inside. If you have to make papers for two classes of 27 and 25, you have 1(27+25) or 1(27) +1(25), 2 pieces would be 2(27+25)=2(27)+2(25), etc. So then generalize it to two classes with x students and y students, and we want to give 4 pieces to each student, so we have 4(x+y) we distribute (multiply) the 4 to get 4x + 4y.
      (11 votes)
  • aqualine ultimate style avatar for user Ryliem123
    can you explain distributive property
    (3 votes)
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    • duskpin sapling style avatar for user proxima
      The distributive property says that when 2 quantities that are being added or subtracted and are multiplied as a whole by another quantity, that quantity is multiplied by every term that is being added/subtracted. That doesn't really make a lot of sense without an example, so let me explain with one.

      2(3x + 2)

      In the above example, we see two quantities being added (3x and 2) and, as a whole, being multiplied by another quantity (2). What the distributive property says is that the above expression is the same as:

      2(3x) + 2(2)

      Which you would then simplify to get 6x + 4.

      If the two quantities in parentheses are being subtracted, the process would still be the same, but the sign would be different. For example:

      5(2x - 3)

      In this expression, we would multiply 5 by each term, but we would subtract those products and we would get this as the answer:

      10x - 15

      Here are a few expressions where the distributive property can be used:

      - 4(4y - 3)
      - 5(5 + 3) (you could just add 5 and 3 first and that would, in my opinion, be easier, but you could also use the distributive property for this)
      - 1/2(5x + 2)
      - both of the examples provided above
      - others following this format

      Here are a few expressions where the distributive property cannot be used:

      - 18 + (3x - 8) (you don't need those parentheses, but I'm just trying to prove a point here)
      - 9(3/2)
      - 6(5*2)
      - others following formats of above expressions in this list


      Hope this helps! :)
      (7 votes)
  • blobby green style avatar for user kdominguez2022
    What would you do if the problem is 18+3w?
    (2 votes)
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  • blobby green style avatar for user Lila
    Sometimes ours are negative, how can you tell that from a subtraction sign?
    (3 votes)
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    • mr pink green style avatar for user David Severin
      negatives and minuses are the same operation, so it all depends on where it is in the expression or equation. Negatives generally come at the beginning of things (front of expression, front of parentheses, or front of denominator), so in the expression -2(-3)/-6 would all be considered negatives. If it is between things, it is considered as a minus, so 3 - 5 is minus. Then you have the special case of minus a negative such as 4 - (-4) which ends up as a positive 4+4.
      (4 votes)
  • hopper cool style avatar for user owenkat
    14k + 35 = ? I don't understand this one. Can someone help me out here?
    (2 votes)
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    • stelly blue style avatar for user Kim Seidel
      Factoring is the opposite of using the distributive property to multiply. If you had: 7(3x + 8), you would distribut the 7 and multiply it both both terms.
      7(3x + 8) = 7(3x) + 7(8) = 21x + 56

      Factoring reverses that process. You start by finding the largest common factor. For 21x + 56, the largest common factor (GCF) = 7. We factor it out by putting 7 in front and by dividing each term by 7.
      21x + 56 = 7 (21x/7 + 56/7) = 7(3x+8)

      Now, see if you can factor you expression. I'll get you started. your GCF = 7.
      Hope this helps.
      (4 votes)
  • mr pants teal style avatar for user Katie Thomas
    Does the order of factoring change in any problems? Or is it always the FOIL method?
    (3 votes)
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    • hopper happy style avatar for user ikrobin
      You do not have to use the foil method. You can use the distributive property, a table/area model, or foil. Each method works. There are some problems that are easy to use foil, and some that are not. There are some problems where you might want to factor a GCF out first to make the numbers more manageable.
      (2 votes)
  • blobby green style avatar for user caleb.flerlage
    so basically were just rewriting the equation in another form?
    (2 votes)
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  • duskpin sapling style avatar for user ReadingHal
    Let's say we have the expression 12 +32y, and you factored it into 4(3+8y). If you factored the expression into 4(8y+3), would it be the same as the first factorization? could you use it as a correct answer?
    (3 votes)
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Video transcript

What I want to do is start with an expression like 4x plus 18 and see if we can rewrite this as the product of two expressions. Essentially, we're going to try to factor this. And the key here is to figure out are there any common factors to both 4x and 18? And we can factor that common factor out. We're essentially going to be reversing the distributive property. So for example, what is the largest number that is-- or I could really say the largest expression-- that is divisible into both 4x and 18? Well, 4x is divisible by 2, because we know that 4 is divisible by 2. And 18 is also divisible by 2, so we can rewrite 4x as being 2 times 2x. If you multiply that side, it's obviously going to be 4x. And then, we can write 18 as the same thing as 2 times 9. And now it might be clear that when you apply the distributive property, you'll usually end up with a step that looks something like this. Now we're just going to undistribute the two right over here. We're going to factor the two out. Let me actually just draw that. So we're going to factor the two out, and so this is going to be 2 times 2x plus 9. And if you were to-- wanted to multiply this out, it would be 2 times 2x plus 2 times 9. It would be exactly this, which you would simplify as this, right up here. So there we have it. We have written this as the product of two expressions, 2 times 2x plus 9. Let's do this again. So let's say that I have 12 plus-- let me think of something interesting-- 32x. Actually since we-- just to get a little bit of variety here, let's put a y here, 12 plus 32y. Well, what's the largest number that's divisible into both 12 and 32? 2 is clearly divisible into both, but so is 4. And let's see. It doesn't look like anything larger than 4 is divisible into both 12 and 32. The greatest common factor of 12 and 32 is 4, and y is only divisible into the second term, not into this first term right over here. So it looks like 4 is the greatest common factor. So we could rewrite each of these as a product of 4 and something else. So for example, 12, we can rewrite as 4 times 3. And 32, we can rewrite-- since it's going to be plus-- 4 times. Well if you divide 32y by 4, it's going to be 8y. And now once again, we can factor out the 4. So this is going to be 4 times 3 plus 8y. And once you do more and more examples of this, you're going to find that you can just do this stuff all at once. You can say hey, what's the largest number that's divisible into both of these? Well, it's 4, so let me factor a 4 out. 12 divided by 4 is 3. 32y divided by 4 is 8y.