Class 8 Exam > Class 8 Notes > Mathematics (Maths) Class 8 > RS Aggarwal Solutions: Exercise 6E - Operations on Algebraic Expressions
RS Aggarwal Solutions: Exercise 6E - Operations on Algebraic Expressions | Mathematics (Maths) Class 8 PDF Download
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Page 1
re
Page 2
re
(-6a + 6b + c -4)
S o l u t i o n :
c
(-6a + 17b)
6a +4b -c +3 +2b -3c +4 -7a +11b +2c -1 -5a +2c -6
¯
-6a +17b + 0c +0
Q u e s t i o n : 7 8
Tick
? the correct answer:
(3q + 7p
2
- 2r
3
+ 4) - (4p
2
- 2q + 7r
3
- 3) = ?
a
(p
2
+ 2q + 5r
3
+ 1)
b
(11p
2
+ q + 5r
3
+ 1)
c
(-3p
2
- 5q + 9r
3
- 7)
d
(3p
2
+ 5q - 9r
3
+7)
S o l u t i o n :
d
(3p
2
+ 5q - 9r
3
+7)
7p
2
+3q -2r
3
+4 4p
2
-2q +7r
3
-3 - + - +
¯
3p
2
+ 5q -9r
3
+ 7
Q u e s t i o n : 7 9
Tick
? the correct answer:
(x + 5)x -3
= ?
a
x
2
+ 5x - 15
b
x
2
- 3x - 15
c
x
2
+ 2x + 15
d
x
2
+ 2x - 15
S o l u t i o n :
d
x
2
+ 2x - 15
(x +5)(x -3) ? (x)(x -3)+(5)(x -3) ? x
2
-3x +5x -15 ? x
2
+2x -15
Q u e s t i o n : 8 0
Tick
? the correct answer:
(2x + 3)(3x - 1) = ?
a
(6x
2
+ 8x - 3)
b
(6x
2
+ 7x - 3)
c
6x
2
- 7x - 3
d
(6x
2
- 7x + 3)
S o l u t i o n :
b
(6x
2
+ 7x - 3)
(2x +3)(3x -1) ? (2x)(3x -1)+(3)(3x -1) ? 6x
2
-2x +9x -3 ? 6x
2
+7x -3
Q u e s t i o n : 8 1
Tick
? the correct answer:
(x + 4)(x + 4) = ?
a
(x
2
+ 16)
b
(x
2
+ 4x + 16)
c
(x
2
+ 8x + 16)
d
(x
2
+ 16x)
S o l u t i o n :
c
(x
2
+ 8x + 16)
(x +4)(x +4) ? (x +4)
2
according to the formula (a +b)
2
= a
2
+2ab +b
2
? x
2
+2(x)(4)+(4)
2
? x
2
+8x +16
Q u e s t i o n : 8 2
Tick
( ) ( )
Page 3
re
(-6a + 6b + c -4)
S o l u t i o n :
c
(-6a + 17b)
6a +4b -c +3 +2b -3c +4 -7a +11b +2c -1 -5a +2c -6
¯
-6a +17b + 0c +0
Q u e s t i o n : 7 8
Tick
? the correct answer:
(3q + 7p
2
- 2r
3
+ 4) - (4p
2
- 2q + 7r
3
- 3) = ?
a
(p
2
+ 2q + 5r
3
+ 1)
b
(11p
2
+ q + 5r
3
+ 1)
c
(-3p
2
- 5q + 9r
3
- 7)
d
(3p
2
+ 5q - 9r
3
+7)
S o l u t i o n :
d
(3p
2
+ 5q - 9r
3
+7)
7p
2
+3q -2r
3
+4 4p
2
-2q +7r
3
-3 - + - +
¯
3p
2
+ 5q -9r
3
+ 7
Q u e s t i o n : 7 9
Tick
? the correct answer:
(x + 5)x -3
= ?
a
x
2
+ 5x - 15
b
x
2
- 3x - 15
c
x
2
+ 2x + 15
d
x
2
+ 2x - 15
S o l u t i o n :
d
x
2
+ 2x - 15
(x +5)(x -3) ? (x)(x -3)+(5)(x -3) ? x
2
-3x +5x -15 ? x
2
+2x -15
Q u e s t i o n : 8 0
Tick
? the correct answer:
(2x + 3)(3x - 1) = ?
a
(6x
2
+ 8x - 3)
b
(6x
2
+ 7x - 3)
c
6x
2
- 7x - 3
d
(6x
2
- 7x + 3)
S o l u t i o n :
b
(6x
2
+ 7x - 3)
(2x +3)(3x -1) ? (2x)(3x -1)+(3)(3x -1) ? 6x
2
-2x +9x -3 ? 6x
2
+7x -3
Q u e s t i o n : 8 1
Tick
? the correct answer:
(x + 4)(x + 4) = ?
a
(x
2
+ 16)
b
(x
2
+ 4x + 16)
c
(x
2
+ 8x + 16)
d
(x
2
+ 16x)
S o l u t i o n :
c
(x
2
+ 8x + 16)
(x +4)(x +4) ? (x +4)
2
according to the formula (a +b)
2
= a
2
+2ab +b
2
? x
2
+2(x)(4)+(4)
2
? x
2
+8x +16
Q u e s t i o n : 8 2
Tick
( ) ( )
? the correct answer:
(x - 6)(x - 6) = ?
a
(x
2
- 36)
b
(x
2
+ 36)
c
(x
2
- 6x + 36)
d
(x
2
- 12x + 36)
S o l u t i o n :
d
(x
2
- 12x + 36)
(x -6)(x -6) ? (x -6)
2
according to the formula (a -b)
2
= a
2
-2ab +b
2
? x
2
-2(x)(6)+(6)
2
? x
2
-12x +36
Q u e s t i o n : 8 3
Tick
? the correct answer:
(2x + 5)(2x - 5) = ?
a
(4x
2
+ 25)
b
(4x
2
- 25)
c
(4x
2
- 10x + 25)
d
(4x
2
+ 10x - 25)
S o l u t i o n :
b
(4x
2
- 25)
(2x +5)(2x -5) ? (2x)
2
-(5)
2
according to the formula (a +b)(a -b) = a
2
-b
2
? 4x
2
- 25
Q u e s t i o n : 8 4
Tick
? the correct answer:
8a
2
b
3
÷ (-2ab) = ?
a
4ab
2
b
4a
2
b
c
-4ab
2
d
-4a
2
b
S o l u t i o n :
c
-4ab
2
8a
2
b
3
÷ (-2ab) ?
8
-2
a
2-1
b
3-1
? -4ab
2
Q u e s t i o n : 8 5
Tick
? the correct answer:
(2x
2
+ 3x + 1) ÷ (x + 1) = ?
a
(x + 1)
b
(2x + 1)
c
(x + 3)
d
(2x + 3)
S o l u t i o n :
b
(2x + 1)
Q u e s t i o n : 8 6
Tick
? the correct answer:
(x
2
- 4x + 4) ÷ (x - 2) = ?
a
(x - 2)
( ) ( )
( )
( )
( ) ( )
Page 4
re
(-6a + 6b + c -4)
S o l u t i o n :
c
(-6a + 17b)
6a +4b -c +3 +2b -3c +4 -7a +11b +2c -1 -5a +2c -6
¯
-6a +17b + 0c +0
Q u e s t i o n : 7 8
Tick
? the correct answer:
(3q + 7p
2
- 2r
3
+ 4) - (4p
2
- 2q + 7r
3
- 3) = ?
a
(p
2
+ 2q + 5r
3
+ 1)
b
(11p
2
+ q + 5r
3
+ 1)
c
(-3p
2
- 5q + 9r
3
- 7)
d
(3p
2
+ 5q - 9r
3
+7)
S o l u t i o n :
d
(3p
2
+ 5q - 9r
3
+7)
7p
2
+3q -2r
3
+4 4p
2
-2q +7r
3
-3 - + - +
¯
3p
2
+ 5q -9r
3
+ 7
Q u e s t i o n : 7 9
Tick
? the correct answer:
(x + 5)x -3
= ?
a
x
2
+ 5x - 15
b
x
2
- 3x - 15
c
x
2
+ 2x + 15
d
x
2
+ 2x - 15
S o l u t i o n :
d
x
2
+ 2x - 15
(x +5)(x -3) ? (x)(x -3)+(5)(x -3) ? x
2
-3x +5x -15 ? x
2
+2x -15
Q u e s t i o n : 8 0
Tick
? the correct answer:
(2x + 3)(3x - 1) = ?
a
(6x
2
+ 8x - 3)
b
(6x
2
+ 7x - 3)
c
6x
2
- 7x - 3
d
(6x
2
- 7x + 3)
S o l u t i o n :
b
(6x
2
+ 7x - 3)
(2x +3)(3x -1) ? (2x)(3x -1)+(3)(3x -1) ? 6x
2
-2x +9x -3 ? 6x
2
+7x -3
Q u e s t i o n : 8 1
Tick
? the correct answer:
(x + 4)(x + 4) = ?
a
(x
2
+ 16)
b
(x
2
+ 4x + 16)
c
(x
2
+ 8x + 16)
d
(x
2
+ 16x)
S o l u t i o n :
c
(x
2
+ 8x + 16)
(x +4)(x +4) ? (x +4)
2
according to the formula (a +b)
2
= a
2
+2ab +b
2
? x
2
+2(x)(4)+(4)
2
? x
2
+8x +16
Q u e s t i o n : 8 2
Tick
( ) ( )
? the correct answer:
(x - 6)(x - 6) = ?
a
(x
2
- 36)
b
(x
2
+ 36)
c
(x
2
- 6x + 36)
d
(x
2
- 12x + 36)
S o l u t i o n :
d
(x
2
- 12x + 36)
(x -6)(x -6) ? (x -6)
2
according to the formula (a -b)
2
= a
2
-2ab +b
2
? x
2
-2(x)(6)+(6)
2
? x
2
-12x +36
Q u e s t i o n : 8 3
Tick
? the correct answer:
(2x + 5)(2x - 5) = ?
a
(4x
2
+ 25)
b
(4x
2
- 25)
c
(4x
2
- 10x + 25)
d
(4x
2
+ 10x - 25)
S o l u t i o n :
b
(4x
2
- 25)
(2x +5)(2x -5) ? (2x)
2
-(5)
2
according to the formula (a +b)(a -b) = a
2
-b
2
? 4x
2
- 25
Q u e s t i o n : 8 4
Tick
? the correct answer:
8a
2
b
3
÷ (-2ab) = ?
a
4ab
2
b
4a
2
b
c
-4ab
2
d
-4a
2
b
S o l u t i o n :
c
-4ab
2
8a
2
b
3
÷ (-2ab) ?
8
-2
a
2-1
b
3-1
? -4ab
2
Q u e s t i o n : 8 5
Tick
? the correct answer:
(2x
2
+ 3x + 1) ÷ (x + 1) = ?
a
(x + 1)
b
(2x + 1)
c
(x + 3)
d
(2x + 3)
S o l u t i o n :
b
(2x + 1)
Q u e s t i o n : 8 6
Tick
? the correct answer:
(x
2
- 4x + 4) ÷ (x - 2) = ?
a
(x - 2)
( ) ( )
( )
( )
( ) ( )
b
(x + 2)
c
(2 - x)
d
(2 + x + x
2
)
S o l u t i o n :
a
(x - 2)
Q u e s t i o n : 8 7
Tick
? the correct answer:
(a + 1)(a - 1)(a
2
+ 1) = ?
a
(a
4
- 2a
2
- 1)
b
(a
4
- a
2
- 1)
c
(a
4
- 1)
d
(a
4
+ 1)
S o l u t i o n :
c
(a
4
- 1)
(i) (a +1)(a -1) a
2
+1 ? (a)
2
-(1)
2
a
2
+1 according to the formula a
2
-b
2
= (a +b)(a -b) ? a
2
-1 a
2
+1 ? a
2
2
- 1
2
2
according to the formula a
2
-b
2
= (a +b)(a -b) ?
Q u e s t i o n : 8 8
Tick
? the correct answer:
1
x
+
1
y
1
x
-
1
y
= ?
a
1
x
2
-
1
y
2
b
1
x
2
+
1
y
2
c
1
x
2
+
1
y
2
-
1
xy
d
1
x
2
-
1
y
2
+
1
xy
S o l u t i o n :
a)
(
1
x
2
-
1
y
2
)
(
1
x
+
1
y
)(
1
( ) ( ) ( ) [ ] ( ) ( ) ( ) ( ) [ ]
( ) ( )
( )
( )
( )
( )
Page 5
re
(-6a + 6b + c -4)
S o l u t i o n :
c
(-6a + 17b)
6a +4b -c +3 +2b -3c +4 -7a +11b +2c -1 -5a +2c -6
¯
-6a +17b + 0c +0
Q u e s t i o n : 7 8
Tick
? the correct answer:
(3q + 7p
2
- 2r
3
+ 4) - (4p
2
- 2q + 7r
3
- 3) = ?
a
(p
2
+ 2q + 5r
3
+ 1)
b
(11p
2
+ q + 5r
3
+ 1)
c
(-3p
2
- 5q + 9r
3
- 7)
d
(3p
2
+ 5q - 9r
3
+7)
S o l u t i o n :
d
(3p
2
+ 5q - 9r
3
+7)
7p
2
+3q -2r
3
+4 4p
2
-2q +7r
3
-3 - + - +
¯
3p
2
+ 5q -9r
3
+ 7
Q u e s t i o n : 7 9
Tick
? the correct answer:
(x + 5)x -3
= ?
a
x
2
+ 5x - 15
b
x
2
- 3x - 15
c
x
2
+ 2x + 15
d
x
2
+ 2x - 15
S o l u t i o n :
d
x
2
+ 2x - 15
(x +5)(x -3) ? (x)(x -3)+(5)(x -3) ? x
2
-3x +5x -15 ? x
2
+2x -15
Q u e s t i o n : 8 0
Tick
? the correct answer:
(2x + 3)(3x - 1) = ?
a
(6x
2
+ 8x - 3)
b
(6x
2
+ 7x - 3)
c
6x
2
- 7x - 3
d
(6x
2
- 7x + 3)
S o l u t i o n :
b
(6x
2
+ 7x - 3)
(2x +3)(3x -1) ? (2x)(3x -1)+(3)(3x -1) ? 6x
2
-2x +9x -3 ? 6x
2
+7x -3
Q u e s t i o n : 8 1
Tick
? the correct answer:
(x + 4)(x + 4) = ?
a
(x
2
+ 16)
b
(x
2
+ 4x + 16)
c
(x
2
+ 8x + 16)
d
(x
2
+ 16x)
S o l u t i o n :
c
(x
2
+ 8x + 16)
(x +4)(x +4) ? (x +4)
2
according to the formula (a +b)
2
= a
2
+2ab +b
2
? x
2
+2(x)(4)+(4)
2
? x
2
+8x +16
Q u e s t i o n : 8 2
Tick
( ) ( )
? the correct answer:
(x - 6)(x - 6) = ?
a
(x
2
- 36)
b
(x
2
+ 36)
c
(x
2
- 6x + 36)
d
(x
2
- 12x + 36)
S o l u t i o n :
d
(x
2
- 12x + 36)
(x -6)(x -6) ? (x -6)
2
according to the formula (a -b)
2
= a
2
-2ab +b
2
? x
2
-2(x)(6)+(6)
2
? x
2
-12x +36
Q u e s t i o n : 8 3
Tick
? the correct answer:
(2x + 5)(2x - 5) = ?
a
(4x
2
+ 25)
b
(4x
2
- 25)
c
(4x
2
- 10x + 25)
d
(4x
2
+ 10x - 25)
S o l u t i o n :
b
(4x
2
- 25)
(2x +5)(2x -5) ? (2x)
2
-(5)
2
according to the formula (a +b)(a -b) = a
2
-b
2
? 4x
2
- 25
Q u e s t i o n : 8 4
Tick
? the correct answer:
8a
2
b
3
÷ (-2ab) = ?
a
4ab
2
b
4a
2
b
c
-4ab
2
d
-4a
2
b
S o l u t i o n :
c
-4ab
2
8a
2
b
3
÷ (-2ab) ?
8
-2
a
2-1
b
3-1
? -4ab
2
Q u e s t i o n : 8 5
Tick
? the correct answer:
(2x
2
+ 3x + 1) ÷ (x + 1) = ?
a
(x + 1)
b
(2x + 1)
c
(x + 3)
d
(2x + 3)
S o l u t i o n :
b
(2x + 1)
Q u e s t i o n : 8 6
Tick
? the correct answer:
(x
2
- 4x + 4) ÷ (x - 2) = ?
a
(x - 2)
( ) ( )
( )
( )
( ) ( )
b
(x + 2)
c
(2 - x)
d
(2 + x + x
2
)
S o l u t i o n :
a
(x - 2)
Q u e s t i o n : 8 7
Tick
? the correct answer:
(a + 1)(a - 1)(a
2
+ 1) = ?
a
(a
4
- 2a
2
- 1)
b
(a
4
- a
2
- 1)
c
(a
4
- 1)
d
(a
4
+ 1)
S o l u t i o n :
c
(a
4
- 1)
(i) (a +1)(a -1) a
2
+1 ? (a)
2
-(1)
2
a
2
+1 according to the formula a
2
-b
2
= (a +b)(a -b) ? a
2
-1 a
2
+1 ? a
2
2
- 1
2
2
according to the formula a
2
-b
2
= (a +b)(a -b) ?
Q u e s t i o n : 8 8
Tick
? the correct answer:
1
x
+
1
y
1
x
-
1
y
= ?
a
1
x
2
-
1
y
2
b
1
x
2
+
1
y
2
c
1
x
2
+
1
y
2
-
1
xy
d
1
x
2
-
1
y
2
+
1
xy
S o l u t i o n :
a)
(
1
x
2
-
1
y
2
)
(
1
x
+
1
y
)(
1
( ) ( ) ( ) [ ] ( ) ( ) ( ) ( ) [ ]
( ) ( )
( )
( )
( )
( )
x
-
1
y
)
? According to the formula (a +b)(a -b) = (a)
2
-(b)
2
: ?
(
1
x
2
-
1
y
2
)
Q u e s t i o n : 8 9
Tick
? the correct answer:
If x +
1
x
= 5
, then x
2
+
1
x
2
= ?
a
25
b
27
c
23
d
25
1
25
S o l u t i o n :
c
23
x +
1
x
= 5 ? Squaring both the sides: ? x +
1
x
2
= (5)
2
? x
2
+
1
x
2
+2(x)
1
x
= 25 ? x
2
+
1
x
2
+2 = 25 ? x
2
+
1
x
2
= 25 -2 ? x
2
+
1
x
2
= 23
Q u e s t i o n : 9 0
Tick
? the correct answer:
If x -
1
x
= 6
, then x
2
+
1
x
2
= ?
a
36
b
38
c
32
d
36
1
36
S o l u t i o n :
b
38
x -
1
x
= 6 ? Squaring both the sides: ? x -
1
x
2
= (6)
2
? x
2
+
1
x
2
-2(x)
1
x
= 36 ? x
2
+
1
x
2
-2 = 36 ? x
2
+
1
x
2
= 36 +2 ? x
2
+
1
x
2
= 38
Q u e s t i o n : 9 1
Tick
? the correct answer:
82
2
- 18
2
= ?
a
8218
b
6418
c
6400
d
7204
S o l u t i o n :
c
6400
(82)
2
-(18)
2
= (82 + 18)(82 - 18) = (100)(64) = 6400
[using the identity
( - )
( )
( )
( ) ( ) ( ( ) ) ( ) ( ) ( )
( )
( )
( ) ( ) ( ( ) ) ( ) ( ) ( )
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Document Description: RS Aggarwal Solutions: Exercise 6E - Operations on Algebraic Expressions for Class 8 2024 is part of Mathematics (Maths) Class 8 preparation.
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