Distributive Property

Show your work for each problem.

1.
Which expression is equivalent to ?
1. a)
2. b)
3. c)
4. d)
Answer:
Using the distributive property: . The factor 2 multiplies both 3 and 5.
2.
Simplify:
Answer: 50
3.
What is expanded?
1. a)
2. b)
3. c)
4. d)
Answer:
. Both terms inside the parentheses are multiplied by 3.
4.
Expand:
Answer: 4y + 12
1. What is ? 4y
2. What is ? 12
3. Combine the results with a plus sign. What is the final answer? 4y + 12
5.
Use the distributive property to calculate: (Hint: )
Answer: 84
6.
Expand:
1. a)
2. b)
3. c)
4. d)
Answer:
. The minus sign stays because it's part of the subtraction.
7.
Expand and give the coefficient of .
Answer: 15
. The coefficient of is .
8.
Expand:
Answer: -2x - 10
1. What is ? -2x
2. What is ? -10
3. Write the final expanded form: -2x - 10
9.
What is expanded?
1. a)
2. b)
3. c)
4. d)
Answer:
. The double negative becomes positive!
10.
Use the distributive property to calculate:
Answer: 792
1. Rewrite 99 as 1
2. What is ? 800
3. What is ? 8
4. What is ? 792
11.
What is the constant term when you expand ?
Answer: -28
. The constant term is .
12.
Expand:
1. a)
2. b)
3. c)
4. d)
Answer:
. The double negative gives a positive.
13.
Expand and simplify: . What is the coefficient of ?
Answer: 5
. The coefficient of is .
14.
Expand:
Answer: -10y + 15
1. What is ? -10y
2. What is ? 15
3. Write the final answer: -10y + 15
15.
Calculate using the distributive property:
Answer: 618
16.
A shop sells gift boxes. Each box contains 3 chocolates at 2 euros each and 2 candies at 1 euro each. Using the distributive property, what is the total cost of 5 boxes?
1. a)30 euros
2. b)45 euros
3. c)40 euros
4. d)35 euros
Answer: 40 euros
Cost per box: euros. For 5 boxes: euros.
17.
Expand and simplify:
Answer: 4x + 14
1. Expand : 6x + 12
2. Expand : -2x + 2
3. Combine: . Collect the terms: 4x
4. Collect the constant terms: 14
5. Write the final simplified answer: 4x + 14
18.
Expand: . Write your answer with the terms in alphabetical order.
Answer: 2a + 2b + 2c
. The distributive property works with any number of terms!