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### Course: 6th grade (Eureka Math/EngageNY) > Unit 4

Lesson 3: Topic D: Expanding, factoring, and distributing expressions- Expression value intuition
- Expression value intuition
- Expression value intuition
- Terms, factors, & coefficients
- Parts of algebraic expressions
- Terms, factors, and coefficients review
- Intro to combining like terms
- Combining like terms
- Combining like terms example
- Combining like terms
- Combining like terms with distribution
- Combining like terms with distribution
- Distributive property over addition
- Distributive property over subtraction
- Factor with the distributive property
- Factor with the distributive property (no variables)
- Distributive property with variables
- Distributive property with variables
- Create equivalent expressions by factoring
- Factor with distributive property (variables)
- Equivalent expressions
- Equivalent expressions

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# Factor with the distributive property

The distributive property helps us factor out the greatest common factor (GCF) in math problems. By finding the GCF of two numbers, we can rewrite the expression as a product, making calculations easier. Understanding this property is essential for simplifying expressions and solving equations.

## Want to join the conversation?

- why do we have to learn math like this we will never need it(116 votes)
- Why can’t we just add and get the answer? It’s easier. 35 plus 50= 85. I don’t want to go with that process every time I add.(32 votes)
- This isn't to find the sum, it's to find the greatest common factor which is useful in different ways. It's applied to later algebruh.(8 votes)

- How can we use distributive property in everyday life senarios - as I'm struggling finding a use for it?(28 votes)
- Going to the grocery store and buying a pound of grapes and 2 pounds of coffee beans. Otherwise, it just helps you with problem solving skills and creative thinking.(1 vote)

- why has my father not returned with the milk? it has been 13 years.(11 votes)
- We first need to find the greatest common factor of 13 years and the amount of milk your father is buying. He is going to buy a gallon of milk from a grocery store and he has taken 13 years so far. We can estimate that he would have bought 5800 gallons of milk. Now, we can solve 5800 divided by 13 to figure out the greatest common factor.(9 votes)

- is five hondred times five hudred 1,0000(8 votes)
- no five hundred would be 250,000. 200 times 50 would be 10,000.

I hope this helps!(11 votes)

- what does it mean when it says to factor out the greatest common factor? what is a common factor or the greatest common factor? I'm a little lost?(8 votes)
- The greatest common factor is the largest integer that you can divide both numbers by to get an integer.(6 votes)

- what do you do if the numbers do have a factor in common for example 75+50(8 votes)
- 75 = 5 x 15 = 5 x (3 x 5) = 3 x 5 x 5

50 = 2 x 25 = 2 x (5 x 5) = 2 x 5 x 5

The two numbers have 5 x 5 (or 25) in common.

75+50=25(3+2)(8 votes)

- If you don't get this, try Euclid's GCF algorithm:

How to Find the GCF of 2 numbers (call them A and B, and

**make sure A>B**)

2. Do A/B. Call the remainder R. Then do R/A. Call the remainder S. Then do S/R. Call the remainder T. And so on, you see what my (or actually, Euclid's) point is? In a nutshell, divide the 2 numbers and divide the remainder by the divisor (the number outside the symbol, or "outside the house").

3. When you come to an equation with no remainder, the divisor (of that equation)is the GCF.

Hope this helps!(7 votes)- this is confusing me(2 votes)

- What if, it was 16+36 I can't find a common factor in those what do I do?(7 votes)
- Also one is always a factor, may not be the largest factor, but is still a factor(0 votes)

- When i click on replay video, It never does anything.(6 votes)

## Video transcript

- [Voiceover] We're asked
to apply the distributive property to factor out the
greatest common factor, and we have 35 plus 50 is equal to, so let me get my scratch pad out. So we have 35 plus 50 is equal to, now what is the greatest
common factor of 35 and 50. So what's the largest whole number that's divisible into both of these. Well I could write 35 as, let's see, I could write that as five times seven, and I could write 50 as five times ten, and so we see five is the
greatest common factor. Seven and ten don't have
any factors in common. So I could rewrite this, I could write 35 as
equal to five times seven and I could rewrite 50 as equal to, get another color here, I could rewrite 50 as five times ten, and of course, I'm adding them, so I have plus right over here. If I want, I could put parentheses, but order of operations would make me do the multiplication first, anyway. But now I want to factor out
that greatest common factor. I want to factor out the five. So what I'm really doing right over here is I'm unwinding the
distributive property. So if I factor out a five,
this is going to be equal to, this is going to be equal to
let's factor out the five. Five times, so you do 35 divided by five, you're just left with the seven. You're just left with the seven over here. So you're just left with the seven after you've factored out the five, and over here, you're
just left with the ten. So five, or seven plus ten, and we're done. 35 plus 50 is equal to
five times seven plus ten. So let me now go and type that in. So this is the same thing as five, five times seven plus ten. And you know you've factored out the greatest common factor because seven and ten don't have any
factors in common anymore. They're called relatively prime. They have no factors in
common other than one. So we could now check that. Let's do a couple more of these. Apply the distributive
property to factor out the greatest common factor. So let's see if we can just do
this one a little bit faster. So let's see, the largest
number it's divisible, in both 75 and 20, I don't
know, let me try five. So if I say five times,
so 75 divided by five, let's see is going to
be, it's going to be 15. Is that right? Yeah, cause five times ten
is 50, five times five is 25. Yeah, so it's 15, and I got that 15 by dividing 75 by five. So 15 plus, and then 20
divided by five would be, 20 divided by five would be four. 15 plus four. Let's see, did I do this right? 15 and four don't have
any factors in common, and if I were to apply the
distributive property here, I'd have five times 15 is 75. Five times four is 20. Yeah, I'm feeling good about that. We got it right.