Class 8 Exam > Class 8 Notes > Mathematics (Maths) Class 8 > RS Aggarwal Solutions: Exercise 6C - Operations on Algebraic Expressions
RS Aggarwal Solutions: Exercise 6C - Operations on Algebraic Expressions | Mathematics (Maths) Class 8 PDF Download
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Page 1
Q u e s t i o n : 4 7
Divide:
i
24x
2
y
3
by 3xy
ii
36xyz
2
by -9xz
iii
-72x
2
y
2
z by -12xyz
iv
-56mnp
2
by 7mnp
S o l u t i o n :
i 24x
2
y
3
by 3xy
24x
2
y
3
3xy
?
24
3
x
2-1
y
3-1
? 8xy
2
.
Therefore, the quotient is 8xy
2
.
ii 36xyz
2
by -9xz
36xyz
2
-9xz
?
36
-9
x
1-1
y
1-0
z
2-1
? -4yz
Therefore, the quotient is -4yz.
iii
-72x
2
y
2
z by -12xyz
-72x
2
y
2
z
-12xyz
?
-72
-12
x
2-1
y
2-1
z
1-1
? 6xy
Therefore, the quotient is 6xy.
iv
-56mnp
2
by 7mnp
-56mnp
2
7mnp
?
-56
7
m
1-1
n
1-1
p
2-1
? -8p
Therefore, the quotient is -8p.
Q u e s t i o n : 4 8
Divide:
i
5m
3
- 30m
2
+ 45m by 5m
ii
8x
2
y
2
- 6xy
2
+ 10x
2
y
3
by 2xy
iii
9x
2
y - 6xy + 12xy
2
by - 3xy
iv
( )
( ) ( )
( )
( ) ( ) ( )
( )
( ) ( ) ( )
( )
( ) ( ) ( )
Page 2
Q u e s t i o n : 4 7
Divide:
i
24x
2
y
3
by 3xy
ii
36xyz
2
by -9xz
iii
-72x
2
y
2
z by -12xyz
iv
-56mnp
2
by 7mnp
S o l u t i o n :
i 24x
2
y
3
by 3xy
24x
2
y
3
3xy
?
24
3
x
2-1
y
3-1
? 8xy
2
.
Therefore, the quotient is 8xy
2
.
ii 36xyz
2
by -9xz
36xyz
2
-9xz
?
36
-9
x
1-1
y
1-0
z
2-1
? -4yz
Therefore, the quotient is -4yz.
iii
-72x
2
y
2
z by -12xyz
-72x
2
y
2
z
-12xyz
?
-72
-12
x
2-1
y
2-1
z
1-1
? 6xy
Therefore, the quotient is 6xy.
iv
-56mnp
2
by 7mnp
-56mnp
2
7mnp
?
-56
7
m
1-1
n
1-1
p
2-1
? -8p
Therefore, the quotient is -8p.
Q u e s t i o n : 4 8
Divide:
i
5m
3
- 30m
2
+ 45m by 5m
ii
8x
2
y
2
- 6xy
2
+ 10x
2
y
3
by 2xy
iii
9x
2
y - 6xy + 12xy
2
by - 3xy
iv
( )
( ) ( )
( )
( ) ( ) ( )
( )
( ) ( ) ( )
( )
( ) ( ) ( )
12x
4
+ 8x
3
- 6x
2
by - 2x
2
S o l u t i o n :
i
5m
3
- 30m
2
+ 45m by 5m
5m
3
-30m
2
+45m ÷ 5m ?
5m
3
5m
-
30m
2
5m
+
45m
5m
? m
2
-6m + 9
Therefore, the quotient is m
2
- 6m + 9.
ii
8x
2
y
2
- 6xy
2
+ 10x
2
y
3
by 2xy
8x
2
y
2
- 6xy
2
+ 10x
2
y
3
÷ 2xy ?
8x
2
y
2
2xy
-
6xy
2
2xy
+
10x
2
y
3
2xy
? 4xy - 3y + 5xy
2
Therefore, the quotient is 4xy - 3y + 5xy
2
.
iii
9x
2
y - 6xy + 12xy
2
by - 3xy
9x
2
y - 6xy + 12xy
2
÷ -3xy ?
9x
2
y
-3xy
-
6xy
-3xy
+
12xy
2
-3xy
? -3x + 2 -4y
Therefore, the quotient is -3x + 2 - 4y.
iv
12x
4
+ 8x
3
- 6x
2
by - 2x
2
12x
4
+ 8x
3
- 6x
2
÷ - 2x
2
?
12x 4
-2x 2
+
8x 3
-2x 2
-
6x 2
-2x 2
? - 6x
2
-4x+3
2
Therefore the quotient is -6x
2
- 4x + 3.
Q u e s t i o n : 4 9
Write the quotient and remainder when we divide:
(x
2
- 4x + 4) by (x - 2)
S o l u t i o n :
Therefore, the quotient is (x -2)
and the remainder is 0.
Q u e s t i o n : 5 0
Write the quotient and remainder when we divide:
(x
2
- 4) by (x + 2)
S o l u t i o n :
Therefore, the quotient is x
-2 and the remainder is 0.
Q u e s t i o n : 5 1
Write the quotient and remainder when we divide:
(x
2
+ 12x + 35) by (x + 7)
S o l u t i o n :
(x
2
+ 12x + 35) by (x + 7)
Therefore, the quotient is (x +5)
and the remainder is 0.
Q u e s t i o n : 5 2
Write the quotient and remainder when we divide:
(15x
2
+ x - 6) by (3x + 2)
( )
( )
( )
( )
Page 3
Q u e s t i o n : 4 7
Divide:
i
24x
2
y
3
by 3xy
ii
36xyz
2
by -9xz
iii
-72x
2
y
2
z by -12xyz
iv
-56mnp
2
by 7mnp
S o l u t i o n :
i 24x
2
y
3
by 3xy
24x
2
y
3
3xy
?
24
3
x
2-1
y
3-1
? 8xy
2
.
Therefore, the quotient is 8xy
2
.
ii 36xyz
2
by -9xz
36xyz
2
-9xz
?
36
-9
x
1-1
y
1-0
z
2-1
? -4yz
Therefore, the quotient is -4yz.
iii
-72x
2
y
2
z by -12xyz
-72x
2
y
2
z
-12xyz
?
-72
-12
x
2-1
y
2-1
z
1-1
? 6xy
Therefore, the quotient is 6xy.
iv
-56mnp
2
by 7mnp
-56mnp
2
7mnp
?
-56
7
m
1-1
n
1-1
p
2-1
? -8p
Therefore, the quotient is -8p.
Q u e s t i o n : 4 8
Divide:
i
5m
3
- 30m
2
+ 45m by 5m
ii
8x
2
y
2
- 6xy
2
+ 10x
2
y
3
by 2xy
iii
9x
2
y - 6xy + 12xy
2
by - 3xy
iv
( )
( ) ( )
( )
( ) ( ) ( )
( )
( ) ( ) ( )
( )
( ) ( ) ( )
12x
4
+ 8x
3
- 6x
2
by - 2x
2
S o l u t i o n :
i
5m
3
- 30m
2
+ 45m by 5m
5m
3
-30m
2
+45m ÷ 5m ?
5m
3
5m
-
30m
2
5m
+
45m
5m
? m
2
-6m + 9
Therefore, the quotient is m
2
- 6m + 9.
ii
8x
2
y
2
- 6xy
2
+ 10x
2
y
3
by 2xy
8x
2
y
2
- 6xy
2
+ 10x
2
y
3
÷ 2xy ?
8x
2
y
2
2xy
-
6xy
2
2xy
+
10x
2
y
3
2xy
? 4xy - 3y + 5xy
2
Therefore, the quotient is 4xy - 3y + 5xy
2
.
iii
9x
2
y - 6xy + 12xy
2
by - 3xy
9x
2
y - 6xy + 12xy
2
÷ -3xy ?
9x
2
y
-3xy
-
6xy
-3xy
+
12xy
2
-3xy
? -3x + 2 -4y
Therefore, the quotient is -3x + 2 - 4y.
iv
12x
4
+ 8x
3
- 6x
2
by - 2x
2
12x
4
+ 8x
3
- 6x
2
÷ - 2x
2
?
12x 4
-2x 2
+
8x 3
-2x 2
-
6x 2
-2x 2
? - 6x
2
-4x+3
2
Therefore the quotient is -6x
2
- 4x + 3.
Q u e s t i o n : 4 9
Write the quotient and remainder when we divide:
(x
2
- 4x + 4) by (x - 2)
S o l u t i o n :
Therefore, the quotient is (x -2)
and the remainder is 0.
Q u e s t i o n : 5 0
Write the quotient and remainder when we divide:
(x
2
- 4) by (x + 2)
S o l u t i o n :
Therefore, the quotient is x
-2 and the remainder is 0.
Q u e s t i o n : 5 1
Write the quotient and remainder when we divide:
(x
2
+ 12x + 35) by (x + 7)
S o l u t i o n :
(x
2
+ 12x + 35) by (x + 7)
Therefore, the quotient is (x +5)
and the remainder is 0.
Q u e s t i o n : 5 2
Write the quotient and remainder when we divide:
(15x
2
+ x - 6) by (3x + 2)
( )
( )
( )
( )
S o l u t i o n :
Therefore, the quotient is (5x -3)
and the remainder is 0.
Q u e s t i o n : 5 3
Write the quotient and remainder when we divide:
(14x
2
- 53x + 45) by (7x - 9)
S o l u t i o n :
Therefore, the quotient is (2x - 5)
and the remainder is 0.
Q u e s t i o n : 5 4
Write the quotient and remainder when we divide:
(6x
2
- 31x + 47) by (2x - 5)
S o l u t i o n :
Therefore, the quotient is (3x - 8)
and the remainder is 7.
Q u e s t i o n : 5 5
Write the quotient and remainder when we divide:
(2x
3
+ x
2
- 5x - 2) by (2x + 3)
S o l u t i o n :
Therefore, the quotient is x
2
-x -1
and the remainder is 1.
Q u e s t i o n : 5 6
Write the quotient and remainder when we divide:
(x
3
+ 1) by (x + 1)
S o l u t i o n :
Therefore, the quotient is x
2
-x+1 and the remainder is 0.
Q u e s t i o n : 5 7
Write the quotient and remainder when we divide:
(x
4
- 2x
3
+ 2x
2
+ x + 4) by (x
2
+ x + 1)
S o l u t i o n :
Therefore, the quotient is ( x
2
- 3x + 4) and remainder is 0.
( )
Page 4
Q u e s t i o n : 4 7
Divide:
i
24x
2
y
3
by 3xy
ii
36xyz
2
by -9xz
iii
-72x
2
y
2
z by -12xyz
iv
-56mnp
2
by 7mnp
S o l u t i o n :
i 24x
2
y
3
by 3xy
24x
2
y
3
3xy
?
24
3
x
2-1
y
3-1
? 8xy
2
.
Therefore, the quotient is 8xy
2
.
ii 36xyz
2
by -9xz
36xyz
2
-9xz
?
36
-9
x
1-1
y
1-0
z
2-1
? -4yz
Therefore, the quotient is -4yz.
iii
-72x
2
y
2
z by -12xyz
-72x
2
y
2
z
-12xyz
?
-72
-12
x
2-1
y
2-1
z
1-1
? 6xy
Therefore, the quotient is 6xy.
iv
-56mnp
2
by 7mnp
-56mnp
2
7mnp
?
-56
7
m
1-1
n
1-1
p
2-1
? -8p
Therefore, the quotient is -8p.
Q u e s t i o n : 4 8
Divide:
i
5m
3
- 30m
2
+ 45m by 5m
ii
8x
2
y
2
- 6xy
2
+ 10x
2
y
3
by 2xy
iii
9x
2
y - 6xy + 12xy
2
by - 3xy
iv
( )
( ) ( )
( )
( ) ( ) ( )
( )
( ) ( ) ( )
( )
( ) ( ) ( )
12x
4
+ 8x
3
- 6x
2
by - 2x
2
S o l u t i o n :
i
5m
3
- 30m
2
+ 45m by 5m
5m
3
-30m
2
+45m ÷ 5m ?
5m
3
5m
-
30m
2
5m
+
45m
5m
? m
2
-6m + 9
Therefore, the quotient is m
2
- 6m + 9.
ii
8x
2
y
2
- 6xy
2
+ 10x
2
y
3
by 2xy
8x
2
y
2
- 6xy
2
+ 10x
2
y
3
÷ 2xy ?
8x
2
y
2
2xy
-
6xy
2
2xy
+
10x
2
y
3
2xy
? 4xy - 3y + 5xy
2
Therefore, the quotient is 4xy - 3y + 5xy
2
.
iii
9x
2
y - 6xy + 12xy
2
by - 3xy
9x
2
y - 6xy + 12xy
2
÷ -3xy ?
9x
2
y
-3xy
-
6xy
-3xy
+
12xy
2
-3xy
? -3x + 2 -4y
Therefore, the quotient is -3x + 2 - 4y.
iv
12x
4
+ 8x
3
- 6x
2
by - 2x
2
12x
4
+ 8x
3
- 6x
2
÷ - 2x
2
?
12x 4
-2x 2
+
8x 3
-2x 2
-
6x 2
-2x 2
? - 6x
2
-4x+3
2
Therefore the quotient is -6x
2
- 4x + 3.
Q u e s t i o n : 4 9
Write the quotient and remainder when we divide:
(x
2
- 4x + 4) by (x - 2)
S o l u t i o n :
Therefore, the quotient is (x -2)
and the remainder is 0.
Q u e s t i o n : 5 0
Write the quotient and remainder when we divide:
(x
2
- 4) by (x + 2)
S o l u t i o n :
Therefore, the quotient is x
-2 and the remainder is 0.
Q u e s t i o n : 5 1
Write the quotient and remainder when we divide:
(x
2
+ 12x + 35) by (x + 7)
S o l u t i o n :
(x
2
+ 12x + 35) by (x + 7)
Therefore, the quotient is (x +5)
and the remainder is 0.
Q u e s t i o n : 5 2
Write the quotient and remainder when we divide:
(15x
2
+ x - 6) by (3x + 2)
( )
( )
( )
( )
S o l u t i o n :
Therefore, the quotient is (5x -3)
and the remainder is 0.
Q u e s t i o n : 5 3
Write the quotient and remainder when we divide:
(14x
2
- 53x + 45) by (7x - 9)
S o l u t i o n :
Therefore, the quotient is (2x - 5)
and the remainder is 0.
Q u e s t i o n : 5 4
Write the quotient and remainder when we divide:
(6x
2
- 31x + 47) by (2x - 5)
S o l u t i o n :
Therefore, the quotient is (3x - 8)
and the remainder is 7.
Q u e s t i o n : 5 5
Write the quotient and remainder when we divide:
(2x
3
+ x
2
- 5x - 2) by (2x + 3)
S o l u t i o n :
Therefore, the quotient is x
2
-x -1
and the remainder is 1.
Q u e s t i o n : 5 6
Write the quotient and remainder when we divide:
(x
3
+ 1) by (x + 1)
S o l u t i o n :
Therefore, the quotient is x
2
-x+1 and the remainder is 0.
Q u e s t i o n : 5 7
Write the quotient and remainder when we divide:
(x
4
- 2x
3
+ 2x
2
+ x + 4) by (x
2
+ x + 1)
S o l u t i o n :
Therefore, the quotient is ( x
2
- 3x + 4) and remainder is 0.
( )
Q u e s t i o n : 5 8
Write the quotient and remainder when we divide:
(x
3
- 6x
2
+ 11x - 6) by (x
2
- 5x + 6)
S o l u t i o n :
Therefore, the quotient is (x-1) and the remainder is 0.
Q u e s t i o n : 5 9
Write the quotient and remainder when we divide:
(5x
3
- 12x
2
+ 12x + 13) by (x
2
- 3x + 4)
S o l u t i o n :
Therefore, the quotient is ( 5x+ 3) and the remainder is (x + 1).
Q u e s t i o n : 6 0
Write the quotient and remainder when we divide:
(2x
3
- 5x
2
+ 8x - 5) by (2x
2
- 3x + 5)
S o l u t i o n :
Therefore, the quotient is (x-1) and the remainder is 0.
Q u e s t i o n : 6 1
Write the quotient and remainder when we divide:
(8x
4
+ 10x
3
- 5x
2
- 4x + 1) by (2x
2
+ x - 1)
S o l u t i o n :
Therefore, the quotient is ( 4x
2
+ 3x -2) and the remainder is ( x-1).
( ) ( ) ( [ ( ]
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Document Description: RS Aggarwal Solutions: Exercise 6C - Operations on Algebraic Expressions for Class 8 2024 is part of Mathematics (Maths) Class 8 preparation.
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students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
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The content of RS Aggarwal Solutions: Exercise 6C - Operations on Algebraic Expressions is prepared as per the latest Class 8 syllabus.
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