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.
The EduRev App will make your learning easier as you can access it from anywhere you want.
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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