USING DISTRIBUTIVE PROPERTY TO SIMPLIFY EXPRESSIONS WORKSHEET  

Simplify the following expressions :

Question 1 :

5 - 3(7x + 8)

Question 2 :

-9a - (1/3)(-3/4 -2a/3 + 12)

Question 3 :

(2a - 3b + c) - 2(4b - 3a + c)

Question 4 :

14 + 5(x + 3) - 7x + 2

1. Answer :

5 - 3(7x + 8)

Step 1 : 

Use the Distributive Property.

5 - 21x - 24

Step 2 :

Rewrite subtraction as adding the opposite.

5 + (-21x) + (-24)

Step 3 :

Use the Commutative Property.

5 + (-24) + (-21x)

Step 4 :

Combine like terms.

- 19 - 21x

Hence, 

5 - 3(7x + 8)  =  - 19 - 21x

2. Answer :

-9a - (1/3)(-3/4 -2a/3 + 12)

Step 1 : 

Use the Distributive Property.

-9a + 1/4 + 2a/9 - 4

Step 2 :

Rewrite subtraction as adding the opposite.

-9a + 1/4 + 2a/9 + (-4)

Step 3 :

Use the Commutative Property.

-9a + 2a/9 + 1/4 + (-4)

Step 4 :

Combine like terms.

- 79a/9 - 15/4

Hence, 

-9a + 1/4 + 2a/9 - 4  = - 79a/9 - 15/4

3. Answer :

(2a - 3b + c) - 2(4b - 3a + c)

Step 1 : 

Use the Distributive Property.

2a - 3b + c - 8b + 6a - 2c

Step 2 : 

Group the like terms 

(2a + 6a) + (-3b - 8b) + (c - 2c) 

Step 3 :

Simplify

8a - 11b - c 

Hence, 

(2a - 3b + c) - 2(4b - 3a + c)  =  8a - 11b - c 

4. Answer :

14 + 5(x + 3) - 7x + 2

Step 1 : 

Use the Distributive Property.

14x + 5x + 15 - 7x + 2

Step 2 : 

Group the like terms 

(14x + 5x - 7x) + (15 + 2) 

Step 3 :

Simplify

11x + 17 

Hence, 

14 + 5(x + 3) - 7x  =  11x + 17

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