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Math Problems
Grade 6
Factor numerical expressions using the distributive property
(
21
−
11
)
{
−
15
+
3
[
4
−
2
(
7
−
9
)
]
}
(21-11)\{-15+3[4-2(7-9)]\}
(
21
−
11
)
{
−
15
+
3
[
4
−
2
(
7
−
9
)]}
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20
−
8
−
3
×
(
9
−
7
)
=
20-8-3 \times(9-7)=
20
−
8
−
3
×
(
9
−
7
)
=
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Factor
99
−
45
f
+
36
b
99-45f+36b
99
−
45
f
+
36
b
to identify the equivalent expressions.
\newline
Choose
2
2
2
answers:
\newline
A)
9
(
11
−
5
f
+
4
b
)
9(11-5f+4b)
9
(
11
−
5
f
+
4
b
)
\newline
B)
3
(
33
−
15
+
12
)
3(33-15+12)
3
(
33
−
15
+
12
)
\newline
C)
11
(
9
−
4
f
+
3
b
)
11(9-4f+3b)
11
(
9
−
4
f
+
3
b
)
\newline
D)
3
(
33
−
15
f
+
12
b
)
3(33-15f+12b)
3
(
33
−
15
f
+
12
b
)
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Factor completely:
\newline
(
3
x
+
4
)
(
2
x
−
3
)
+
(
5
x
+
2
)
(
2
x
−
3
)
2
(3 x+4)(2 x-3)+(5 x+2)(2 x-3)^{2}
(
3
x
+
4
)
(
2
x
−
3
)
+
(
5
x
+
2
)
(
2
x
−
3
)
2
\newline
Answer:
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Factor completely:
\newline
(
x
+
8
)
(
2
x
+
9
)
2
−
(
2
x
+
9
)
(
2
x
+
7
)
(x+8)(2 x+9)^{2}-(2 x+9)(2 x+7)
(
x
+
8
)
(
2
x
+
9
)
2
−
(
2
x
+
9
)
(
2
x
+
7
)
\newline
Answer:
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Factor completely:
\newline
(
x
−
4
)
(
4
x
−
7
)
−
(
x
−
4
)
2
(
x
−
8
)
(x-4)(4 x-7)-(x-4)^{2}(x-8)
(
x
−
4
)
(
4
x
−
7
)
−
(
x
−
4
)
2
(
x
−
8
)
\newline
Answer:
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Factor completely:
\newline
(
x
+
4
)
(
5
x
−
9
)
+
(
4
x
−
7
)
(
x
+
4
)
(x+4)(5 x-9)+(4 x-7)(x+4)
(
x
+
4
)
(
5
x
−
9
)
+
(
4
x
−
7
)
(
x
+
4
)
\newline
Answer:
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Factor completely:
\newline
(
x
+
4
)
2
−
(
9
x
+
1
)
2
(x+4)^{2}-(9 x+1)^{2}
(
x
+
4
)
2
−
(
9
x
+
1
)
2
\newline
Answer:
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Factor completely:
\newline
(
x
+
1
)
2
−
(
5
x
−
8
)
2
(x+1)^{2}-(5 x-8)^{2}
(
x
+
1
)
2
−
(
5
x
−
8
)
2
\newline
Answer:
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Factor completely:
\newline
(
6
x
−
7
)
2
−
(
x
+
4
)
2
(6 x-7)^{2}-(x+4)^{2}
(
6
x
−
7
)
2
−
(
x
+
4
)
2
\newline
Answer:
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Factor completely:
\newline
(
8
x
−
9
)
2
−
(
x
+
5
)
2
(8 x-9)^{2}-(x+5)^{2}
(
8
x
−
9
)
2
−
(
x
+
5
)
2
\newline
Answer:
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Factor completely:
\newline
(
x
−
2
)
2
−
(
10
x
+
7
)
2
(x-2)^{2}-(10 x+7)^{2}
(
x
−
2
)
2
−
(
10
x
+
7
)
2
\newline
Answer:
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Factor completely:
\newline
(
10
x
−
7
)
2
−
(
3
x
+
2
)
2
(10 x-7)^{2}-(3 x+2)^{2}
(
10
x
−
7
)
2
−
(
3
x
+
2
)
2
\newline
Answer:
Get tutor help
Factor completely:
\newline
(
4
x
−
1
)
2
−
(
x
+
10
)
2
(4 x-1)^{2}-(x+10)^{2}
(
4
x
−
1
)
2
−
(
x
+
10
)
2
\newline
Answer:
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Factor completely:
\newline
4
x
2
(
3
x
+
4
)
−
(
3
x
+
4
)
4 x^{2}(3 x+4)-(3 x+4)
4
x
2
(
3
x
+
4
)
−
(
3
x
+
4
)
\newline
Answer:
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Factor completely:
\newline
5
x
(
4
x
+
3
)
+
2
(
4
x
+
3
)
5 x(4 x+3)+2(4 x+3)
5
x
(
4
x
+
3
)
+
2
(
4
x
+
3
)
\newline
Answer:
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Factor completely:
\newline
16
x
2
(
x
2
−
5
)
−
9
(
x
2
−
5
)
16 x^{2}\left(x^{2}-5\right)-9\left(x^{2}-5\right)
16
x
2
(
x
2
−
5
)
−
9
(
x
2
−
5
)
\newline
Answer:
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Factor completely:
\newline
4
x
2
(
x
+
8
)
−
7
(
x
+
8
)
4 x^{2}(x+8)-7(x+8)
4
x
2
(
x
+
8
)
−
7
(
x
+
8
)
\newline
Answer:
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Factor completely:
\newline
2
x
(
x
+
8
)
+
7
(
x
+
8
)
2 x(x+8)+7(x+8)
2
x
(
x
+
8
)
+
7
(
x
+
8
)
\newline
Answer:
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Factor completely:
\newline
x
2
(
x
2
+
3
)
−
x
(
x
2
+
3
)
−
2
(
x
2
+
3
)
x^{2}\left(x^{2}+3\right)-x\left(x^{2}+3\right)-2\left(x^{2}+3\right)
x
2
(
x
2
+
3
)
−
x
(
x
2
+
3
)
−
2
(
x
2
+
3
)
\newline
Answer:
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Factor completely:
\newline
6
x
(
3
x
−
10
)
+
5
(
3
x
−
10
)
6 x(3 x-10)+5(3 x-10)
6
x
(
3
x
−
10
)
+
5
(
3
x
−
10
)
\newline
Answer:
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Factor completely:
\newline
25
x
2
(
x
2
+
3
)
−
9
(
x
2
+
3
)
25 x^{2}\left(x^{2}+3\right)-9\left(x^{2}+3\right)
25
x
2
(
x
2
+
3
)
−
9
(
x
2
+
3
)
\newline
Answer:
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Factor completely:
\newline
(
8
x
−
7
)
2
−
(
2
x
+
1
)
2
(8 x-7)^{2}-(2 x+1)^{2}
(
8
x
−
7
)
2
−
(
2
x
+
1
)
2
\newline
Answer:
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Factor completely:
\newline
7
(
8
x
+
9
)
3
−
(
8
x
+
9
)
4
7(8 x+9)^{3}-(8 x+9)^{4}
7
(
8
x
+
9
)
3
−
(
8
x
+
9
)
4
\newline
Answer:
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Factor completely:
\newline
10
(
6
x
+
7
)
6
−
(
6
x
+
7
)
7
10(6 x+7)^{6}-(6 x+7)^{7}
10
(
6
x
+
7
)
6
−
(
6
x
+
7
)
7
\newline
Answer:
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Factor completely:
\newline
5
(
x
+
4
)
2
+
(
x
+
4
)
3
5(x+4)^{2}+(x+4)^{3}
5
(
x
+
4
)
2
+
(
x
+
4
)
3
\newline
Answer:
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Factor completely:
\newline
(
x
−
8
)
5
+
(
x
−
8
)
6
(x-8)^{5}+(x-8)^{6}
(
x
−
8
)
5
+
(
x
−
8
)
6
\newline
Answer:
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Factor completely:
\newline
(
x
+
9
)
5
−
5
(
x
+
9
)
4
(x+9)^{5}-5(x+9)^{4}
(
x
+
9
)
5
−
5
(
x
+
9
)
4
\newline
Answer:
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Factor completely:
\newline
3
(
10
x
+
7
)
+
(
10
x
+
7
)
2
3(10 x+7)+(10 x+7)^{2}
3
(
10
x
+
7
)
+
(
10
x
+
7
)
2
\newline
Answer:
Get tutor help
Factor completely:
\newline
10
(
x
+
9
)
4
−
(
x
+
9
)
5
10(x+9)^{4}-(x+9)^{5}
10
(
x
+
9
)
4
−
(
x
+
9
)
5
\newline
Answer:
Get tutor help
Factor completely:
\newline
(
x
−
7
)
5
+
8
(
x
−
7
)
4
(x-7)^{5}+8(x-7)^{4}
(
x
−
7
)
5
+
8
(
x
−
7
)
4
\newline
Answer:
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Factor completely:
\newline
2
(
4
x
−
3
)
4
+
(
4
x
−
3
)
5
2(4 x-3)^{4}+(4 x-3)^{5}
2
(
4
x
−
3
)
4
+
(
4
x
−
3
)
5
\newline
Answer:
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Solve for
x
\mathrm{x}
x
.
\newline
2
x
+
5
8
+
2
x
+
1
24
=
7
\frac{2 x+5}{8}+\frac{2 x+1}{24}=7
8
2
x
+
5
+
24
2
x
+
1
=
7
\newline
Answer:
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Which equation has the same solution as
x
2
−
8
x
−
12
=
7
x^{2}-8 x-12=7
x
2
−
8
x
−
12
=
7
?
\newline
(
x
−
4
)
2
=
35
(x-4)^{2}=35
(
x
−
4
)
2
=
35
\newline
(
x
+
4
)
2
=
3
(x+4)^{2}=3
(
x
+
4
)
2
=
3
\newline
(
x
+
4
)
2
=
35
(x+4)^{2}=35
(
x
+
4
)
2
=
35
\newline
(
x
−
4
)
2
=
3
(x-4)^{2}=3
(
x
−
4
)
2
=
3
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Rewrite in simplest terms:
8
(
9
q
−
6
)
+
7
(
−
7
q
+
4
)
8(9 q-6)+7(-7 q+4)
8
(
9
q
−
6
)
+
7
(
−
7
q
+
4
)
\newline
Answer:
Get tutor help
Which ordered pair is a solution of the equation?
\newline
−
3
x
+
4
y
=
14
-3x+4y=14
−
3
x
+
4
y
=
14
\newline
Choose
1
1
1
answer:
\newline
(A) Only
(
2
,
5
)
(2,5)
(
2
,
5
)
\newline
(B) Only
(
4
,
6
)
(4,6)
(
4
,
6
)
\newline
(C) Both
(
2
,
5
)
(2,5)
(
2
,
5
)
and
(
4
,
6
)
(4,6)
(
4
,
6
)
\newline
(D) Neither
Get tutor help
Which of the following is equivalent to
18
18
18
more than the product of
9
−
6
p
9-6p
9
−
6
p
and
p
−
2
p-2
p
−
2
?
\newline
Choose
1
1
1
answer:
\newline
(A)
3
(
7
p
+
6
)
3(7p+6)
3
(
7
p
+
6
)
\newline
(B)
−
3
p
(
2
p
−
7
)
-3p(2p-7)
−
3
p
(
2
p
−
7
)
\newline
(C)
(
27
−
6
p
)
(
p
−
2
)
(27-6p)(p-2)
(
27
−
6
p
)
(
p
−
2
)
\newline
(D)
(
9
−
6
p
)
(
p
+
16
)
(9-6p)(p+16)
(
9
−
6
p
)
(
p
+
16
)
Get tutor help
Factor
24
k
+
36
q
−
12
24 k+36 q-12
24
k
+
36
q
−
12
to identify the equivalent expressions.
\newline
Choose
2
2
2
answers:
\newline
A
12
(
2
k
+
3
q
−
1
)
12(2 k+3 q-1)
12
(
2
k
+
3
q
−
1
)
\newline
B
3
(
8
k
+
12
q
−
4
)
3(8 k+12 q-4)
3
(
8
k
+
12
q
−
4
)
\newline
c
6
(
3
k
+
6
q
−
12
)
6(3 k+6 q-12)
6
(
3
k
+
6
q
−
12
)
\newline
D
12
(
2
k
+
3
q
)
12(2 k+3 q)
12
(
2
k
+
3
q
)
Get tutor help
Factor
60
−
36
w
60-36 w
60
−
36
w
to identify the equivalent expressions.
\newline
Choose
2
2
2
answers:
\newline
A
6
(
10
−
6
w
)
6(10-6 w)
6
(
10
−
6
w
)
\newline
B
4
(
15
−
8
w
)
4(15-8 w)
4
(
15
−
8
w
)
\newline
C
12
(
5
−
3
w
)
12(5-3 w)
12
(
5
−
3
w
)
\newline
D
3
(
20
+
12
w
)
3(20+12 w)
3
(
20
+
12
w
)
Get tutor help
Factor
18
p
−
36
18 p-36
18
p
−
36
to identify the equivalent expressions.
\newline
Choose
2
2
2
answers:
\newline
A
3
(
9
p
−
12
)
3(9 p-12)
3
(
9
p
−
12
)
\newline
B
9
(
2
p
−
4
p
)
9(2 p-4 p)
9
(
2
p
−
4
p
)
\newline
c
2
(
9
p
−
18
)
2(9 p-18)
2
(
9
p
−
18
)
\newline
D
18
(
p
−
2
)
18(p-2)
18
(
p
−
2
)
Get tutor help
Factor
10
h
+
30
+
50
j
10 h+30+50 j
10
h
+
30
+
50
j
to identify the equivalent expressions.
\newline
Choose
2
2
2
answers:
\newline
A
5
(
2
h
+
30
+
50
j
)
5(2 h+30+50 j)
5
(
2
h
+
30
+
50
j
)
\newline
B
10
(
h
+
3
+
5
j
)
10(h+3+5 j)
10
(
h
+
3
+
5
j
)
\newline
c
2
(
5
h
+
15
+
25
j
)
2(5 h+15+25 j)
2
(
5
h
+
15
+
25
j
)
\newline
D
15
(
10
h
+
2
+
50
j
)
15(10 h+2+50 j)
15
(
10
h
+
2
+
50
j
)
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Factor
64
b
−
16
c
64 b-16 c
64
b
−
16
c
to identify the equivalent expressions.
\newline
Choose
2
2
2
answers:
\newline
A
16
(
4
b
−
c
)
16(4 b-c)
16
(
4
b
−
c
)
\newline
B
4
(
16
b
−
4
)
4(16 b-4)
4
(
16
b
−
4
)
\newline
c
8
(
8
b
+
2
c
)
8(8 b+2 c)
8
(
8
b
+
2
c
)
\newline
D
2
(
32
b
−
8
c
)
2(32 b-8 c)
2
(
32
b
−
8
c
)
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Factor
24
j
−
16
24 j-16
24
j
−
16
to identify the equivalent expressions.
\newline
Choose
2
2
2
answers:
\newline
A
8
(
3
j
−
2
)
8(3 j-2)
8
(
3
j
−
2
)
\newline
B
6
(
4
j
−
2
j
)
6(4 j-2 j)
6
(
4
j
−
2
j
)
\newline
C
4
(
6
j
−
4
)
4(6 j-4)
4
(
6
j
−
4
)
\newline
D
2
(
12
−
8
)
2(12-8)
2
(
12
−
8
)
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