Distributive Property And Simplifying Like Terms

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| By Sarah Hartung

Sarah Hartung

Community Contributor

Quizzes Created: 2 | Total Attempts: 2,109

Questions: 10 | Attempts: 803 | Updated: Mar 21, 2023

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Students will demonstate the ability to use the distributive property and combine like terms.

Questions and Answers

1.

5(q-p) expands to become
- A.
  
  5q-5p
- B.
  
  5q-p
- C.
  
  5q+5p
- D.
  
  Q-5p
Correct Answer
A. 5q-5p

Explanation
The given expression, 5(q-p), can be expanded by distributing the 5 to both terms inside the parentheses. This results in 5q - 5p. Therefore, the correct answer is 5q - 5p.

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2.

-4(3x+2) expands to become
- A.
  
  12x-2
- B.
  
  -12x+4
- C.
  
  -12x+8
- D.
  
  -12x-8
Correct Answer
D. -12x-8

Explanation
Expanding -4(3x+2) means multiplying -4 by each term inside the parentheses. Using the distributive property, we get -12x - 8.

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3.

Simplify 5y+7+y
- A.
  
  6y+7
- B.
  
  12y
- C.
  
  5y+8
- D.
  
  4y+7
Correct Answer
A. 6y+7

Explanation
The given expression is 5y+7+y. To simplify it, we can combine the like terms, which are the terms with the same variable (y). When we add 5y and y, we get 6y. Therefore, the simplified form of the expression is 6y+7.

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4.

Simplify 7z+3w-4z+3w+6
- A.
  
  15zw
- B.
  
  3z+6w+6
- C.
  
  11z+6w+6
- D.
  
  3z+6w
Correct Answer
B. 3z+6w+6

Explanation
The given expression is a combination of terms with variables z and w. To simplify the expression, we need to combine like terms. In this case, we have two terms with z (7z and -4z) and two terms with w (3w and 3w). Simplifying these terms, we get 7z - 4z = 3z and 3w + 3w = 6w. Combining these simplified terms with the constant term 6, we get the simplified expression 3z + 6w + 6.

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5.

Simplify and combine like terms for 6(3+2y) + 3y=

Correct Answer
18+15y
15y+18

Explanation
The given expression is 6(3+2y) + 3y. To simplify and combine like terms, we can distribute the 6 to both terms inside the parentheses, which gives us 18+12y. Then, we add 3y to this expression to get 18+15y. Therefore, the correct answer is 18+15y. Another way to write this expression is as 15y+18.

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6.

Simplify and combine like terms for 2(8w-4) +10 =

Correct Answer
16w+2
2+16w

Explanation
To simplify and combine like terms for the given expression, we start by distributing the 2 to both terms inside the parentheses. This gives us 16w - 8 + 10. Simplifying further, we combine like terms by adding -8 and 10, which gives us 2. Therefore, the simplified expression is 16w + 2. The answer provided, 16w + 2, is correct.

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7.

Simplify and combine like terms for 5(x+4y+2x)

Correct Answer
15x+20y
20y+15x

Explanation
The given expression can be simplified by distributing the 5 to each term inside the parentheses. This results in 5x + 20y + 10x. Combining like terms, we can add the x terms together to get 15x, and the y terms together to get 20y. Therefore, the simplified expression is 15x + 20y. The answer 20y + 15x is also correct, as addition is commutative, meaning the order of the terms does not affect the result.

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8.

Simplify and combine like terms for 9(a+b) + 4(3a+2b)

Correct Answer
21a+17b
17b+21a

Explanation
The given expression involves distributing and combining like terms. First, distribute 9 to both a and b in the first term, and distribute 4 to both 3a and 2b in the second term. This gives us 9a + 9b + 12a + 8b. Then, combine like terms by adding the coefficients of a and b separately. This simplifies the expression to 21a + 17b. Therefore, the correct answer is 21a + 17b.

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9.

Simplify and combine like terms for 8(k+m) + 15(2k+5m)

Correct Answer
38k+83m
83m+38k

Explanation
The given expression involves adding two terms: 8(k+m) and 15(2k+5m). To simplify and combine like terms, we distribute the coefficients to each term within the parentheses. This results in 8k + 8m + 30k + 75m. Combining like terms, we get 38k + 83m. Therefore, the correct answer is 38k+83m.

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10.

Simplify and combine like terms for -7(9x + 3y) + 7(3x + 5y)=

Correct Answer
-42x+14y
14y-42x
14y+-42x
14y+(-42x)

Explanation
The given expression involves distributing the -7 and 7 to the terms inside the parentheses. When we simplify and combine like terms, we get -63x - 21y + 21x + 35y. Simplifying further, we get -42x + 14y. Therefore, the correct answer is -42x + 14y.

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Current Version
Mar 21, 2023

Quiz Edited by
ProProfs Editorial Team
Nov 14, 2014

Quiz Created by
Sarah Hartung

Distributive Property And Simplifying Like Terms

5(q-p) expands to become

-4(3x+2) expands to become

Simplify 5y+7+y

Simplify 7z+3w-4z+3w+6

Simplify and combine like terms for 6(3+2y) + 3y=

Simplify and combine like terms for 2(8w-4) +10 =

Simplify and combine like terms for 5(x+4y+2x)

Simplify and combine like terms for 9(a+b) + 4(3a+2b)

Simplify and combine like terms for 8(k+m) + 15(2k+5m)

Simplify and combine like terms for -7(9x + 3y) + 7(3x + 5y)=