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## Algebra (all content)

### Course: Algebra (all content)>Unit 10

Lesson 12: Factoring polynomials by taking common factors

# Factoring with the distributive property

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

## Want to join the conversation?

• how does this help me in real life? • 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 • can you explain distributive property • 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! :)
• can you explain distributive property • 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.
• What would you do if the problem is 18+3w? • Sometimes ours are negative, how can you tell that from a subtraction sign? • 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.
• 14k + 35 = ? I don't understand this one. Can someone help me out here? • 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.
• Does the order of factoring change in any problems? Or is it always the FOIL method? • so basically were just rewriting the equation in another form?  