7th Grade Distributive Property And Symplifying Like Terms
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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 q and -p. 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 When we distribute -4 to each term inside the parentheses, we multiply -4 with each term. This gives us -12x for the first term and -8 for the second term. Therefore, the expanded form of -4(3x+2) is -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 this expression, we can combine the like terms, which are the terms with the same variable, y. Adding 5y and y gives us 6y. The constant term, 7, remains unchanged. 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 can combine like terms. The terms 7z and -4z can be combined to give 3z. Similarly, the terms 3w and 3w can be combined to give 6w. The constant term 6 remains unchanged. Therefore, the simplified expression is 3z + 6w + 6.
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5.
Simplify and combine like terms for 6(3+2y) + 3y=
Correct Answer 18+15y
Explanation To simplify and combine like terms for 6(3+2y) + 3y, we first distribute the 6 to both terms inside the parentheses. This gives us 18 + 12y. Then we add the 3y to this expression, resulting in 18 + 15y.
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6.
Simplify and combine like terms for 2(8w-4) +10 =
Correct Answer 18w+2
Explanation The given expression is 2(8w-4) + 10. To simplify this expression, we first distribute the 2 to both terms inside the parentheses. This gives us 16w - 8 + 10. Combining like terms, we have 16w + 2. Therefore, the simplified expression is 18w + 2.
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7.
Simplify and combine like terms for 5(x+4y+2x)
Correct Answer 15x+20y
Explanation To simplify and combine like terms for 5(x+4y+2x), we distribute the 5 to each term inside the parentheses, resulting in 5x+20y+10x. Then, we combine the like terms, which are the x terms, giving us 15x+20y.
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8.
Simplify and combine like terms for 9(a+b) + 4(3a+2b)
Correct Answer 21a+17b
Explanation The expression 9(a+b) + 4(3a+2b) can be simplified by distributing the coefficients to the terms inside the parentheses. This results in 9a + 9b + 12a + 8b. Combining like terms, we get 21a + 17b.
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9.
Simplify and combine like terms for 8(k+m) + 15(2k+5m)
Correct Answer 38k+73m
Explanation To simplify and combine like terms for 8(k+m) + 15(2k+5m), we distribute the 8 and 15 to each term inside the parentheses. This gives us 8k + 8m + 30k + 75m. Next, we combine like terms by adding the coefficients of the k and m terms. This gives us 38k + 83m. Therefore, the simplified and combined expression is 38k + 73m.
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10.
Simplify and combine like terms for -7(9x + 3y) + 7(3x + 5y)=
Correct Answer -42x+14y
Explanation To simplify and combine like terms for the given expression, we distribute the -7 and 7 to the terms inside the parentheses. This gives us -63x - 21y + 21x + 35y. Then, we combine like terms by adding the coefficients of x and y. This results in -42x + 14y.
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