Simplifying Expressions with the Distributive Property

Simplifying Expressions with the Distributive Property

Distributive Property

• uses multiplication with addition or subtraction

• you can multiply a sum or difference by another number or term

• Example; 6 (x + 3)

•  $6\cdot x+6\cdot3$  
  

•  $6x+18$  

Examples Continued;

Simplify: 8 (a-b)

 $8\cdot a-8\cdot b$  
Answer: 8a-8b

Simplify; -(6n+5)
-1(6n+5)
(-1)6n+(-1)5
Answer: -6n-5

Multiple Choice

Simplify using the Distributive Property:

7(2+y)

 $7\cdot2+7\cdot y$  

• 9+7+y

• 14+7y

Multiple Choice

Simplify

12(t+4)

What is the first step?

• $12\cdot t+4$

• $12\cdot t+12\cdot4$

Multiple Choice

Simplify

2(k+8k)

What is the first step?

• $2\cdot k+2\cdot8+2\cdot k$

• $2\cdot k+2\cdot8k$

Multiple Choice

Now Simplify to the final step;

2(k+8k)

 $2\cdot k+2\cdot8k$  

• 2k+10k

• 2k+16k

Multiple Choice

Simplify using the Distributive Property

4(a-c)

• 4-ac

• 4a-4c

Your turn to practice

complete the practice problems for today in Schoology

Using the Distributive Property & Combine Like Terms

• After using the Distributive Property, check to see if they are "Like Terms" that you can combine

• Example; 7(x+3+2x)

•  $7\cdot x+7\cdot3+7\cdot2x$  

•  $7x+21+14x$  

• Check for like terms; 7x and 14x

• Your final answer is; 21x+21

Multiple Choice

Practice Together;
2 (4x+5+3x)
Step 1:

 $2\cdot4x+2\cdot5+2\cdot3x$  
Step 2: 
 $8x+10+6x$  
Step 3: Check for Like Terms, which ones do I combine?

• 8x, 10

• 10, 6x

• 8x, 6x

Poll

How are you feeling right now?

• I think I get it!!!

• I need more practice

• I have no clue, I'm lost!

Multiple Choice

Simplify this Expression;
5 (x+2+3x)
Step 1:

 $5\cdot x+5\cdot2+5\cdot3x$ 

• 5x+10+15x

• 20x+10
  

• 10x+13x

Multiple Choice

Simplify The Expression;

2 (4y+4+6y)

• 8y+8+12y

• 16y+8

• 20y+8

Multiple Choice

Simplify The Expression;

2 (3x+5+2x+3)

• 10x+10+6

• 6x+10+4x+6

• 10x+16

Multiple Choice

Simplify The Expression;

4(2x+8)

• 8x+8

• 16x

• 6x+12

Poll

How are you feeling now?

• I've got this I am ready to practice on my own!

• I am so lost, don't leave me yet Mrs. Bond!

• I'm not sure, but I am willing to try some by myself...