1. Distributing Expressions
Lesson 12
Distributing
Expressions

2. Let’s Take Notes on Two Methods for Distributing
Tape Diagram – Make tapes to represent the expression. 3(4a+2c) That means I have 4a +2c three times. Make tapes to represent. a c
12a +6c

3. 2nd Method
Area Model – Make a rectangle and break apart the expression. Use length x width to fill in box. 3(4a + 2c)
4 a c 3
12a 6c

4. This is called Distributing the 2 or handing out the 25 3
This picture represents (5+3)
If I want to represent 2(5+3)
I would need to add another 5+3 5 3
Now I have and or groups of 5+3
I can write that 2 ( 5+3)
2(5+3) = 2x5 + 2x3
This is called Distributing the 2 or handing out the 2
2(5+3) = 2 x x 3 The 2 was DISTRIBUTED

5. If I wanted to double the expression I would need another 3x + 2y
2 groups of 3x +2y or 2(3x + 2y)
6x + 4y
2(3x+2y) = (2 · 3x ) + (2 · 2y)
6x + 4y (expanded form)
This is called the DISTRIBUTIVE PROPERTY

6. 3x y 2
2 · 3x 6x
2 · 2y 4y
6x y
Using this model, we can now write the equivalent expression.
We do this by calculating the area of each of the rectangles. Remember: a = lw

7. Now Let’s Try a Few Problems in your Notebooks

8. Both models prove that 2 (p+ z) =2p+ 2z p + z 2 2p + 2z 2 (p + z)
Create two models for the expression and then write an equivalent expression (expanded form).
p + z p z 2
2 · p 2p
2 · z 2z p z
2p + 2z
Both models prove that
2 (p+ z) =2p+ 2z

9. Both models prove that 3 (2a + 3b) =6a + 9b 2a + 3b 3 6a + 9b
Create two models for the expression and then write an equivalent expression (expanded form). .
2a + 3b a b 3
3 · 2a 6a
3 · 3b 9b a b a b
6a + 9b
Both models prove that
3 (2a + 3b) =6a + 9b

10. Let’s try these using the models!!
5 (a + 7b)
2) 2(3p + r)
3) 6(4 +b)
5a + 35 b
6p + 2r
24 + 6b

11. Try these using the models on your OWN!!
4 (g + 7b)
2) 5(3e + t)
3) 2(7 +p)
4g + 28b
g= 5 b= 2
15e + 5t
e= 3 t= 6
14 + 2p
p= 2
Let’s Evaluate these Expressions in our Notebooks to see if they are equivalent!

12. Let’s try a few without using models!!!
4 (4g + 3y) =
16g + 12y
2a (b + 10) =
2ab+ 20a

13. Distributive Property and Factoring Expressions
Lesson 11
Distributive Property and
Factoring Expressions

14. 2x x3
5 + 5
3 + 3 5 3
This picture represents 5+5 and 3+3
Or I could write it
2x5 + 2x3
Can I change the order of these numbers and it still represent the same amount?
YES!!!! 5 3
I can write that 2 ( 5+3)
Now I have and or groups of 5+3
2x5 + 2x3 = 2(5+3)
If you add up the bars in either picture the total is 16. If you follow pemdas in 2(5+3)
2(8) 16
You still get 16
2(5+3) = 2 x x 3 This is called the DISTRIBUTIVE PROPERTY

15. Let’s try Another Example

16. 2x x4
9 + 9
4+ 4 9 4
This picture represents 9+9 and 4+4
Or I could write it
2x9 + 2x4
Can I change the order of these numbers and it still represent the same amount?
YES!!!! 9 4
I can write that 2 ( 9+4)
Now I have and or groups of 9+4
2x9 + 2x4 = 2(9+4)
If you add up the bars in either picture the total is 26. If you follow pemdas in 2(9+4)
2(13) 26
You still get 26
2(9+4) = 2 x x 4 This is called the DISTRIBUTIVE PROPERTY

17. Now Let’s Try A Problem with Variables

18. YES!!!! So a+a + b+b could be written as 2a+2b or 2(a+b)
This picture represents a+a and b+b
Or I could write it
2a + 2b
Can I change the order of these numbers and it still represent the same amount?
YES!!!! a b
Now I have a + b and a + b or groups of a+b
I can write that 2 ( a+b)
So a+a + b+b could be written as 2a+2b or 2(a+b)
If you look at 2a +2b you are really finding what they have in common (GCF) 2 and taking that and putting it in FRONT and then writing the rest of your expression
2a + 2b = 2(a+b) This is called the DISTRIBUTIVE PROPERTY

19. Finding the GCF for Two Expressions and Writing it as ONE EXPRESSION

20. Look at: f and 3g 3
What do they have in common (GCF)? Rewrite the expression taking out the 3(GCF). 3(f+g) 3f + 3g = 3(f+g) Look at: 4p and 4h What do they have in common(GCF)? Rewrite the expression taking out the (GCF) 4(p + h) 4p + 4h = 4(p+h) 4

21. What happens if it DOES NOT look like they have anything in common
Look at: 6x + 9y I will have to break 6x and 9y apart 2 • 3 • x + 3 • 3 • y Now, you can see they have a 3 as the GCF So, let’s take out 3 the GCF 3(2x +3y) 6x + 9y = 3(2x + 3y)

22. 3c + 11c
What do you think the GCF is? C So, let’s take out the GCF C(3+11) 3c+11c = c(3+11)

23. Try this one on your own..
24b + 8 GCF is 8 8(3b+1) 24b + 8 is equal to 8(3b+1)

24. Let’s try the Rest of the Exercises in Your Packet