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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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• how does this help me in real life?
(59 votes)
• I'm wondering the same thing, along with quadratic equations, and Pythagorean theorem.
(34 votes)
• 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
(12 votes)
• You just add the -8 and 9. So -8+9=1.
This gives 14k+1=-13. Subtract 1 from both sides to get 14k= -14.
(12 votes)
• can you explain distributive property
(5 votes)
• 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! :)
(13 votes)
• 1,2 buckle my shoeee 3,4 buckle some moreeee 5,6 nike kicks
(11 votes)
• stop...
(1 vote)
• can you explain distributive property
(4 votes)
• 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.
(13 votes)
• i dont get it everything doesnt make sense
(6 votes)
• hi is anyone watching this in 2023
(5 votes)
• Sort by most recent instead of top voted, and you will see a question 13 days ago.
(3 votes)
• why does math exist
(2 votes)
• Without math, you wouldn't be able to:
1) Count (no more keeping track of scores in sports)
2) Manage money
3) Have smart phones, video games and other things you likely enjoy which all needed math engineer & develop.
4) Discover many scientific developments that help us understand and deal with the real world in medicine, physics, engineering, constructions, business, and many other things.
(9 votes)
• What would you do if the problem is 18+3w?
(2 votes)
• i would prefer not to ask a question
(5 votes)

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.