Class 8 Exam > Class 8 Notes > Mathematics (Maths) Class 8 > RS Aggarwal Solutions: Exercise 6B - Operations on Algebraic Expressions
RS Aggarwal Solutions: Exercise 6B - Operations on Algebraic Expressions | Mathematics (Maths) Class 8 PDF Download
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Page 2
Q u e s t i o n : 2 5
Find the product:
(7x + 2y) × (x + 4y)
S o l u t i o n :
By horizontal method:
7x +2y × x +4y = 7x x +4y +2y x +4y = 7x
2
+28xy +2xy +8y
2
= 7x
2
+30xy +8y
2
Q u e s t i o n : 2 6
Find the product:
(9x + 5y) × (4x + 3y)
S o l u t i o n :
By horizontal method:
9x +5y × 4x +3y 9x 4x +3y +5y 4x +3y = 36x
2
+27xy +20xy +15y
2
= 36x
2
+47xy +15y
2
Q u e s t i o n : 2 7
Find the product:
(3m - 4n) × (2m - 3n)
S o l u t i o n :
By horizontal method:
3m -4n × 2m -3n = 3m 2m -3n -4n 2m -3n = 6m
2
-9mn -8mn +12n
2
= 6m
2
-17mn +12n
2
Q u e s t i o n : 2 8
Find the product:
(x
2
- a
2
) × (x - a)
S o l u t i o n :
By horizontal method:
x
2
-a
2
× x -a = x
2
x -a -a
2
x -a = x
3
-ax
2
-a
2
x +a
3
i.e x
3
+a
3
-ax x -a
Q u e s t i o n : 2 9
Find the product:
(x
2
- y
2
) × (x + 2y)
S o l u t i o n :
By horizontal method:
x
2
-y
2
× x +2y = x
2
x +2y -y
2
x +2y = x
3
+2x
2
y -xy
2
-2y
3
i. e x
3
-2y
3
+xy 2x -y
Q u e s t i o n : 3 0
Find the product:
(3p
2
+ q
2
) × (2p
2
- 3q
2
)
S o l u t i o n :
By horizontal method:
3p
2
+q
2
× 2p
2
-3q
2
= 3p
2
2p
2
-3q
2
+q
2
2p
2
-3q
2
= 6p
4
-9p
2
q
2
+2p
2
q
2
-3q
4
i. e6p
4
-7p
2
q
2
-3q
4
Q u e s t i o n : 3 1
Find the product:
(2x
2
- 5y
2
) × (x
2
+ 3y
2
)
S o l u t i o n :
By horizontal method:
2x
2
-5y
2
× x
2
+3y
2
= 2x
2
x
2
+3y
2
-5y
2
x
2
+3y
2
= 2x
4
+6x
2
y
2
-5x
2
y
2
-15y
4
= 2x
4
+x
2
y
2
-15y
4
Q u e s t i o n : 3 2
Find the product:
(x
3
- y
3
) × (x
2
+ y
2
)
S o l u t i o n :
By horizontal method:
x
3
-y
3
× x
2
+y
2
= x
3
x
2
+y
2
-y
3
x
2
+y
2
= x
5
+x
3
y
2
-x
2
y
3
-y
5
= x
5
-y
5
+x
2
y
2
(x -y)
Q u e s t i o n : 3 3
Find the product:
(x
4
+ y
4
) × (x
2
- y
2
)
S o l u t i o n :
By horizontal method:
x
4
+y
4
× x
2
-y
2
= x
4
x
2
-y
2
+y
4
x
2
-y
2
= x
6
-x
4
y
2
+y
4
x
2
-y
6
= x
6
-y
6
-x
2
y
2
x
2
-y
2
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
Page 3
Q u e s t i o n : 2 5
Find the product:
(7x + 2y) × (x + 4y)
S o l u t i o n :
By horizontal method:
7x +2y × x +4y = 7x x +4y +2y x +4y = 7x
2
+28xy +2xy +8y
2
= 7x
2
+30xy +8y
2
Q u e s t i o n : 2 6
Find the product:
(9x + 5y) × (4x + 3y)
S o l u t i o n :
By horizontal method:
9x +5y × 4x +3y 9x 4x +3y +5y 4x +3y = 36x
2
+27xy +20xy +15y
2
= 36x
2
+47xy +15y
2
Q u e s t i o n : 2 7
Find the product:
(3m - 4n) × (2m - 3n)
S o l u t i o n :
By horizontal method:
3m -4n × 2m -3n = 3m 2m -3n -4n 2m -3n = 6m
2
-9mn -8mn +12n
2
= 6m
2
-17mn +12n
2
Q u e s t i o n : 2 8
Find the product:
(x
2
- a
2
) × (x - a)
S o l u t i o n :
By horizontal method:
x
2
-a
2
× x -a = x
2
x -a -a
2
x -a = x
3
-ax
2
-a
2
x +a
3
i.e x
3
+a
3
-ax x -a
Q u e s t i o n : 2 9
Find the product:
(x
2
- y
2
) × (x + 2y)
S o l u t i o n :
By horizontal method:
x
2
-y
2
× x +2y = x
2
x +2y -y
2
x +2y = x
3
+2x
2
y -xy
2
-2y
3
i. e x
3
-2y
3
+xy 2x -y
Q u e s t i o n : 3 0
Find the product:
(3p
2
+ q
2
) × (2p
2
- 3q
2
)
S o l u t i o n :
By horizontal method:
3p
2
+q
2
× 2p
2
-3q
2
= 3p
2
2p
2
-3q
2
+q
2
2p
2
-3q
2
= 6p
4
-9p
2
q
2
+2p
2
q
2
-3q
4
i. e6p
4
-7p
2
q
2
-3q
4
Q u e s t i o n : 3 1
Find the product:
(2x
2
- 5y
2
) × (x
2
+ 3y
2
)
S o l u t i o n :
By horizontal method:
2x
2
-5y
2
× x
2
+3y
2
= 2x
2
x
2
+3y
2
-5y
2
x
2
+3y
2
= 2x
4
+6x
2
y
2
-5x
2
y
2
-15y
4
= 2x
4
+x
2
y
2
-15y
4
Q u e s t i o n : 3 2
Find the product:
(x
3
- y
3
) × (x
2
+ y
2
)
S o l u t i o n :
By horizontal method:
x
3
-y
3
× x
2
+y
2
= x
3
x
2
+y
2
-y
3
x
2
+y
2
= x
5
+x
3
y
2
-x
2
y
3
-y
5
= x
5
-y
5
+x
2
y
2
(x -y)
Q u e s t i o n : 3 3
Find the product:
(x
4
+ y
4
) × (x
2
- y
2
)
S o l u t i o n :
By horizontal method:
x
4
+y
4
× x
2
-y
2
= x
4
x
2
-y
2
+y
4
x
2
-y
2
= x
6
-x
4
y
2
+y
4
x
2
-y
6
= x
6
-y
6
-x
2
y
2
x
2
-y
2
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
Q u e s t i o n : 3 4
Find the product:
x
4
+
1
x
4
× x +
1
x
S o l u t i o n :
By horizontal method:
x
4
+
1
x
4
× x +
1
x
= x
4
x +
1
x
+
1
x
4
x +
1
x
= x
5
+x
3
+
1
x
3
+
1
x
5
i. e x
3
x
2
+1 +
1
x
3
1 +
1
x
2
Q u e s t i o n : 3 5
Find the product:
(x
2
- 3x + 7) × 2x +3
S o l u t i o n :
By horizontal method:
x
2
-3x +7 × 2x +3 = 2x x
2
-3x +7 +3 x
2
-3x +7 = 2x
3
-6x
2
+14x +3x
2
-9x +21 = 2x
3
-3x
2
+5x +21
Q u e s t i o n : 3 6
Find the product:
(3x
2
+ 5x - 9) × (3x - 5)
S o l u t i o n :
By horizontal method:
3x
2
+5x -9 × 3x -5 = 3x 3x
2
+5x -9 -5 3x
2
+5x -9 = 9x
3
+15x
2
-27x -15x
2
-25x +45 = 9x
3
-52x +45
Q u e s t i o n : 3 7
Find the product:
(x
2
- xy + y
2
) × (x + y)
S o l u t i o n :
By horizontal method:
x
2
-xy +y
2
× x +y = x x
2
-xy +y
2
+y x
2
-xy +y
2
= x
3
-x
2
y +y
2
x +x
2
y -xy
2
+y
3
= x
3
+y
3
Q u e s t i o n : 3 8
Find the product:
(x
2
+ xy + y
2
) × (x - y)
S o l u t i o n :
By horizontal method:
x
2
+xy +y
2
× x -y x x
2
+xy +y
2
-y x
2
+xy +y
2
= x
3
+x
2
y +xy
2
-x
2
y -xy
2
-y
3
= x
3
-y
3
Q u e s t i o n : 3 9
Find the product:
(x
3
- 2x
2
+ 5) × (4x - 1)
S o l u t i o n :
By horizontal method:
x
3
-2x
2
+5 × 4x -1 = 4x x
3
-2x
2
+5 -1 x
3
-2x
2
+5 = 4x
4
-8x
3
+20x -x
3
+2x
2
-5 = 4x
4
-9x
3
+2x
2
+20x -5
Q u e s t i o n : 4 0
Find the product:
(9x
2
- x + 15) × (x
2
- 3)
S o l u t i o n :
By horizontal method:
9x
2
-x +15 × x
2
-3 = x
2
9x
2
-x +15 -3 9x
2
-x +15 = 9x
4
-x
3
+15x
2
-27x
2
+3x -45 = 9x
4
-x
3
-12x
2
+3x -45
Q u e s t i o n : 4 1
Find the product:
(x
2
- 5x + 8) × (x
2
+ 2)
S o l u t i o n :
By horizontal method:
x
2
-5x +8 × x
2
+2 = x
2
x
2
-5x +8 +2 x
2
-5x +8 = x
4
-5x
3
+8x
2
+2x
2
-10x +16 = x
4
-5x
3
+10x
2
-10x +16
Q u e s t i o n : 4 2
Find the product:
(x
3
- 5x
2
+ 3x + 1) × (x
3
- 3)
S o l u t i o n :
By horizontal method:
x
3
-5x
2
+3x +1 × x
2
-3 = x
2
x
3
-5x
2
+3x +1 -3 x
3
-5x
2
+3x +1 = x
5
-5x
4
+3x
3
+x
2
-3x
3
+15x
2
-9x -3 = x
5
-5x
4
+16x
2
-9x -3
Q u e s t i o n : 4 3
Find the product:
( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
Page 4
Q u e s t i o n : 2 5
Find the product:
(7x + 2y) × (x + 4y)
S o l u t i o n :
By horizontal method:
7x +2y × x +4y = 7x x +4y +2y x +4y = 7x
2
+28xy +2xy +8y
2
= 7x
2
+30xy +8y
2
Q u e s t i o n : 2 6
Find the product:
(9x + 5y) × (4x + 3y)
S o l u t i o n :
By horizontal method:
9x +5y × 4x +3y 9x 4x +3y +5y 4x +3y = 36x
2
+27xy +20xy +15y
2
= 36x
2
+47xy +15y
2
Q u e s t i o n : 2 7
Find the product:
(3m - 4n) × (2m - 3n)
S o l u t i o n :
By horizontal method:
3m -4n × 2m -3n = 3m 2m -3n -4n 2m -3n = 6m
2
-9mn -8mn +12n
2
= 6m
2
-17mn +12n
2
Q u e s t i o n : 2 8
Find the product:
(x
2
- a
2
) × (x - a)
S o l u t i o n :
By horizontal method:
x
2
-a
2
× x -a = x
2
x -a -a
2
x -a = x
3
-ax
2
-a
2
x +a
3
i.e x
3
+a
3
-ax x -a
Q u e s t i o n : 2 9
Find the product:
(x
2
- y
2
) × (x + 2y)
S o l u t i o n :
By horizontal method:
x
2
-y
2
× x +2y = x
2
x +2y -y
2
x +2y = x
3
+2x
2
y -xy
2
-2y
3
i. e x
3
-2y
3
+xy 2x -y
Q u e s t i o n : 3 0
Find the product:
(3p
2
+ q
2
) × (2p
2
- 3q
2
)
S o l u t i o n :
By horizontal method:
3p
2
+q
2
× 2p
2
-3q
2
= 3p
2
2p
2
-3q
2
+q
2
2p
2
-3q
2
= 6p
4
-9p
2
q
2
+2p
2
q
2
-3q
4
i. e6p
4
-7p
2
q
2
-3q
4
Q u e s t i o n : 3 1
Find the product:
(2x
2
- 5y
2
) × (x
2
+ 3y
2
)
S o l u t i o n :
By horizontal method:
2x
2
-5y
2
× x
2
+3y
2
= 2x
2
x
2
+3y
2
-5y
2
x
2
+3y
2
= 2x
4
+6x
2
y
2
-5x
2
y
2
-15y
4
= 2x
4
+x
2
y
2
-15y
4
Q u e s t i o n : 3 2
Find the product:
(x
3
- y
3
) × (x
2
+ y
2
)
S o l u t i o n :
By horizontal method:
x
3
-y
3
× x
2
+y
2
= x
3
x
2
+y
2
-y
3
x
2
+y
2
= x
5
+x
3
y
2
-x
2
y
3
-y
5
= x
5
-y
5
+x
2
y
2
(x -y)
Q u e s t i o n : 3 3
Find the product:
(x
4
+ y
4
) × (x
2
- y
2
)
S o l u t i o n :
By horizontal method:
x
4
+y
4
× x
2
-y
2
= x
4
x
2
-y
2
+y
4
x
2
-y
2
= x
6
-x
4
y
2
+y
4
x
2
-y
6
= x
6
-y
6
-x
2
y
2
x
2
-y
2
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
Q u e s t i o n : 3 4
Find the product:
x
4
+
1
x
4
× x +
1
x
S o l u t i o n :
By horizontal method:
x
4
+
1
x
4
× x +
1
x
= x
4
x +
1
x
+
1
x
4
x +
1
x
= x
5
+x
3
+
1
x
3
+
1
x
5
i. e x
3
x
2
+1 +
1
x
3
1 +
1
x
2
Q u e s t i o n : 3 5
Find the product:
(x
2
- 3x + 7) × 2x +3
S o l u t i o n :
By horizontal method:
x
2
-3x +7 × 2x +3 = 2x x
2
-3x +7 +3 x
2
-3x +7 = 2x
3
-6x
2
+14x +3x
2
-9x +21 = 2x
3
-3x
2
+5x +21
Q u e s t i o n : 3 6
Find the product:
(3x
2
+ 5x - 9) × (3x - 5)
S o l u t i o n :
By horizontal method:
3x
2
+5x -9 × 3x -5 = 3x 3x
2
+5x -9 -5 3x
2
+5x -9 = 9x
3
+15x
2
-27x -15x
2
-25x +45 = 9x
3
-52x +45
Q u e s t i o n : 3 7
Find the product:
(x
2
- xy + y
2
) × (x + y)
S o l u t i o n :
By horizontal method:
x
2
-xy +y
2
× x +y = x x
2
-xy +y
2
+y x
2
-xy +y
2
= x
3
-x
2
y +y
2
x +x
2
y -xy
2
+y
3
= x
3
+y
3
Q u e s t i o n : 3 8
Find the product:
(x
2
+ xy + y
2
) × (x - y)
S o l u t i o n :
By horizontal method:
x
2
+xy +y
2
× x -y x x
2
+xy +y
2
-y x
2
+xy +y
2
= x
3
+x
2
y +xy
2
-x
2
y -xy
2
-y
3
= x
3
-y
3
Q u e s t i o n : 3 9
Find the product:
(x
3
- 2x
2
+ 5) × (4x - 1)
S o l u t i o n :
By horizontal method:
x
3
-2x
2
+5 × 4x -1 = 4x x
3
-2x
2
+5 -1 x
3
-2x
2
+5 = 4x
4
-8x
3
+20x -x
3
+2x
2
-5 = 4x
4
-9x
3
+2x
2
+20x -5
Q u e s t i o n : 4 0
Find the product:
(9x
2
- x + 15) × (x
2
- 3)
S o l u t i o n :
By horizontal method:
9x
2
-x +15 × x
2
-3 = x
2
9x
2
-x +15 -3 9x
2
-x +15 = 9x
4
-x
3
+15x
2
-27x
2
+3x -45 = 9x
4
-x
3
-12x
2
+3x -45
Q u e s t i o n : 4 1
Find the product:
(x
2
- 5x + 8) × (x
2
+ 2)
S o l u t i o n :
By horizontal method:
x
2
-5x +8 × x
2
+2 = x
2
x
2
-5x +8 +2 x
2
-5x +8 = x
4
-5x
3
+8x
2
+2x
2
-10x +16 = x
4
-5x
3
+10x
2
-10x +16
Q u e s t i o n : 4 2
Find the product:
(x
3
- 5x
2
+ 3x + 1) × (x
3
- 3)
S o l u t i o n :
By horizontal method:
x
3
-5x
2
+3x +1 × x
2
-3 = x
2
x
3
-5x
2
+3x +1 -3 x
3
-5x
2
+3x +1 = x
5
-5x
4
+3x
3
+x
2
-3x
3
+15x
2
-9x -3 = x
5
-5x
4
+16x
2
-9x -3
Q u e s t i o n : 4 3
Find the product:
( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
(3x + 2y - 4) × (x - y + 2)
S o l u t i o n :
By horizontal method:
3x +2y -4 × x -y +2 x 3x +2y -4 -y 3x +2y -4 +2 3x +2y -4 = 3x
2
+2xy -4x -3xy -2y
2
+4y +6x +4y -8 = 3x
2
-2y
2
-xy +2x +8y -8
Q u e s t i o n : 4 4
Find the product:
(x
2
- 5x + 8) × (x
2
+ 2x - 3)
S o l u t i o n :
By horizontal method:
x
2
-5x +8 × x
2
+2x -3 = x
2
x
2
-5x +8 +2x x
2
-5x +8 -3 x
2
-5x +8 = x
4
-5x
3
+8x
2
+2x
3
-10x
2
+16x -3x
2
+15x -24 = x
4
-3x
3
-5x
2
+31x -24
Q u e s t i o n : 4 5
Find the product:
(2x
2
+ 3x - 7) × (3x
2
- 5x + 4)
S o l u t i o n :
By horizontal method:
2x
2
+3x -7 × 3x
2
-5x +4 = 2x
2
3x
2
-5x +4 +3x 3x
2
-5x +4 -7 3x
2
-5x +4 = 6x
4
-10x
3
+8x
2
+9x
3
-15x
2
+12x -21x
2
+35x -28 = 6x
4
-x
3
-28x
2
+47x -28
Q u e s t i o n : 4 6
Find the product:
(9x
2
- x + 15) × (x
2
- x - 1)
S o l u t i o n :
By horizontal method:
9x
2
-x +15 × x
2
-x -1 = x
2
9x
2
-x +15 -x 9x
2
-x +15 -1 9x
2
-x +15 = 9x
4
-x
3
+15x
2
-9x
3
+x
2
-15x -9x
2
+x -15 = 9x
4
-10x
3
+7x
2
-14x -15
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
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Document Description: RS Aggarwal Solutions: Exercise 6B - Operations on Algebraic Expressions for Class 8 2024 is part of Mathematics (Maths) Class 8 preparation.
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