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### Course: Grade 8 math (FL B.E.S.T.)>Unit 1

Lesson 3: Factoring with the distributive property

# 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?
• I'm wondering the same thing, along with quadratic equations, and Pythagorean theorem.
• why does math exist
• 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.
• 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
• 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.
• 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.
• i dont get it everything doesnt make sense
• i see no real application of this strategy in making toast, taking a shower, or running outside. just sayin. not rlly necessary.
• If you continue to study math, I promise this will be useful! In real life, you might use this if you enter a field in physics, math, engineering, science, or computer science, but for now your main goal in learning this should be to be comfortable with it so you can pick up more difficult math concepts. Starting around Algebra 2 and Precalculus, factoring will become something that needs to come naturally in order to solve more difficult problems.
• What would you do if the problem is 18+3w?
• hi is anyone watching this in 2023
• Sort by most recent instead of top voted, and you will see a question 13 days ago.
• how would you do it with negative numbers in the problem