Class 8 Exam > Class 8 Notes > Mathematics (Maths) Class 8 > RS Aggarwal Solutions: Exercise 7B - Factorisation
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Page 2
We have:
4x
2
-9y
2
= (2x)
2
-(3y)
2
= (2x +3y)(2x -3y)
? 4x
2
-9y
2
= (2x +3y)(2x -3y)
Q u e s t i o n : 3 3
Factorise:
16a
2
- 225b
2
S o l u t i o n :
We have:
16a
2
-225b
2
= (4a)
2
-(15b)
2
= (4a +15b)(4a -15b)
? 16a
2
-225b
2
= (4a +15b)(4a -15b)
Q u e s t i o n : 3 4
Factorise:
9a
2
b
2
- 25
S o l u t i o n :
We have:
9a
2
b
2
-25 = (3ab)
2
-(5)
2
= (3ab +5)(3ab -5)
? 9a
2
b
2
-25 = (3ab +5)(3ab -5)
Q u e s t i o n : 3 5
Factorise:
16a
2
- 144
S o l u t i o n :
We have:
16a
2
-144 = (4a)
2
-(12)
2
= (4a +12)(4a -12) = 4 a + 3 4 a -3 = 16 a +3 a -3
? 16a
2
-144 = 16(a +3)(a -3)
Q u e s t i o n : 3 6
Factorise:
63a
2
- 112b
2
S o l u t i o n :
We have:
63a
2
-112b
2
= 7 9a
2
-16b
2
= 7 (3a)
2
-(4b)
2
= 7(3a +4b)(3a -4b)
? 63a
2
-112b
2
= 7(3a +4b)(3a -4b)
Q u e s t i o n : 3 7
Factorise:
20a
2
- 45b
2
S o l u t i o n :
We have:
20a
2
-45b
2
= 5 4a
2
-9b
2
= 5 (2a)
2
-(3b)
2
= 5(2a +3b)(2a -3b)
? 20a
2
-45b
2
= 5(2a +3b)(2a -3b)
Q u e s t i o n : 3 8
Factorise:
12x
2
- 27
S o l u t i o n :
We have:
12x
2
-27 = 3 4x
2
-9 = 3 (2x)
2
-(3)
2
= 3(2x +3)(2x -3)
? 12x
2
-27 = 3(2x +3)(2x -3)
Q u e s t i o n : 3 9
Factorise:
x
3
- 64x
S o l u t i o n :
We have:
x
3
-64x = x x
2
-64 = x (x)
2
-(8)
2
= x(x +8)(x -8)
? x
3
-64x = x(x +8)(x -8)
Q u e s t i o n : 4 0
Factorise:
16x
5
- 144x
3
S o l u t i o n :
We have:
16x
5
-144x
3
= 16x
3
x
2
-9 = 16x
3
(x)
2
-(3)
2
= 16x
3
(x +3)(x -3)
? 16x
5
-144x
3
= 16x
3
(x +3)(x -3)
Q u e s t i o n : 4 1
( ) ( ) ( ) ( )
( ) { }
( ) { }
( ) { }
( ) { }
( ) { }
Page 3
We have:
4x
2
-9y
2
= (2x)
2
-(3y)
2
= (2x +3y)(2x -3y)
? 4x
2
-9y
2
= (2x +3y)(2x -3y)
Q u e s t i o n : 3 3
Factorise:
16a
2
- 225b
2
S o l u t i o n :
We have:
16a
2
-225b
2
= (4a)
2
-(15b)
2
= (4a +15b)(4a -15b)
? 16a
2
-225b
2
= (4a +15b)(4a -15b)
Q u e s t i o n : 3 4
Factorise:
9a
2
b
2
- 25
S o l u t i o n :
We have:
9a
2
b
2
-25 = (3ab)
2
-(5)
2
= (3ab +5)(3ab -5)
? 9a
2
b
2
-25 = (3ab +5)(3ab -5)
Q u e s t i o n : 3 5
Factorise:
16a
2
- 144
S o l u t i o n :
We have:
16a
2
-144 = (4a)
2
-(12)
2
= (4a +12)(4a -12) = 4 a + 3 4 a -3 = 16 a +3 a -3
? 16a
2
-144 = 16(a +3)(a -3)
Q u e s t i o n : 3 6
Factorise:
63a
2
- 112b
2
S o l u t i o n :
We have:
63a
2
-112b
2
= 7 9a
2
-16b
2
= 7 (3a)
2
-(4b)
2
= 7(3a +4b)(3a -4b)
? 63a
2
-112b
2
= 7(3a +4b)(3a -4b)
Q u e s t i o n : 3 7
Factorise:
20a
2
- 45b
2
S o l u t i o n :
We have:
20a
2
-45b
2
= 5 4a
2
-9b
2
= 5 (2a)
2
-(3b)
2
= 5(2a +3b)(2a -3b)
? 20a
2
-45b
2
= 5(2a +3b)(2a -3b)
Q u e s t i o n : 3 8
Factorise:
12x
2
- 27
S o l u t i o n :
We have:
12x
2
-27 = 3 4x
2
-9 = 3 (2x)
2
-(3)
2
= 3(2x +3)(2x -3)
? 12x
2
-27 = 3(2x +3)(2x -3)
Q u e s t i o n : 3 9
Factorise:
x
3
- 64x
S o l u t i o n :
We have:
x
3
-64x = x x
2
-64 = x (x)
2
-(8)
2
= x(x +8)(x -8)
? x
3
-64x = x(x +8)(x -8)
Q u e s t i o n : 4 0
Factorise:
16x
5
- 144x
3
S o l u t i o n :
We have:
16x
5
-144x
3
= 16x
3
x
2
-9 = 16x
3
(x)
2
-(3)
2
= 16x
3
(x +3)(x -3)
? 16x
5
-144x
3
= 16x
3
(x +3)(x -3)
Q u e s t i o n : 4 1
( ) ( ) ( ) ( )
( ) { }
( ) { }
( ) { }
( ) { }
( ) { }
Factorise:
3x
5
- 48x
3
S o l u t i o n :
We have:
3x
5
-48x
3
= 3x
3
x
2
-16 = 3x
3
(x)
2
-(4)
2
= 3x
3
(x +4)(x -4)
? 3x
5
-48x
3
= 3x
3
(x +4)(x -4)
Q u e s t i o n : 4 2
Factorise:
16p
3
- 4p
S o l u t i o n :
We have:
16p
3
-4p = 4p 4p
2
-1 = 4p (2p)
2
-(1)
2
= 4p(2p +1)(2p -1)
? 16p
3
-4p = 4p(2p +1)(2p -1)
Q u e s t i o n : 4 3
Factorise:
63a
2
b
2
- 7
S o l u t i o n :
We have:
63a
2
b
2
-7 = 7 9a
2
b
2
-1 = 7 (3ab)
2
-(1)
2
= 7(3ab +1)(3ab -1)
? 63a
2
b
2
-7 = 7(3ab +1)(3ab -1)
Q u e s t i o n : 4 4
Factorise:
1 - b -c
2
S o l u t i o n :
We have:
1 -(b -c)
2
= (1)
2
-(b -c)
2
= {1 +(b -c)}{1 -(b -c)} = (1 +b -c)(1 -b +c)
? 1 -(b -c)
2
= (1 +b -c)(1 -b +c)
Q u e s t i o n : 4 5
Factorise:
(2a + 3b)
2
- 16c
2
S o l u t i o n :
We have:
(2a +3b)
2
-16c
2
= (2a +3b)
2
-(4c)
2
= {(2a +3b)+4c}{(2a +3b)-4c} = (2a +3b +4c)(2a +3b -4c)
? (2a +3b)
2
-16c
2
= (2a +3b +4c)(2a +3b -4c)
Q u e s t i o n : 4 6
Factorise:
(l + m)
2
- (l - m)
2
S o l u t i o n :
We have:
(l +m)
2
-(l -m)
2
= {(l +m)+(l -m)}{(l +m)-(l -m)} = (l +m +l -m)(l +m -l +m) = (2l)(2m)
? (l +m)
2
-(l -m)
2
= (2l)(2m)
Q u e s t i o n : 4 7
Factorise:
(2x + 5y)
2
- 1
S o l u t i o n :
We have:
(2x +5y)
2
-1 = (2x +5y)
2
-(1)
2
= {(2x +5y)+1}{(2x +5y)-1} = (2x +5y +1)(2x +5y -1)
? (2x +5y)
2
-1 = (2x +5y +1)(2x +5y -1)
Q u e s t i o n : 4 8
Factorise:
36c
2
- (5a + b)
2
S o l u t i o n :
We have:
36c
2
-(5a +b)
2
= (6c)
2
-(5a +b)
2
= {(6c)+(5a +b)}{(6c)-(5a +b)} = (6c +5a +b)(6c -5a -b)
? 36c
2
-(5a +b)
2
= (6c +5a +b)(6c -5a -b)
Q u e s t i o n : 4 9
Factorise:
(3x - 4y)
2
- 25z
2
S o l u t i o n :
We have:
(3x -4y)
2
-25z
2
= (3x -4y)
2
-(5z)
2
= {(3x -4y)+5z}{(3x -4y)-5z} = (3x -4y +5z)(3x -4y -5z)
? (3x -4y)
2
-25z
2
= (3x -4y +5z)(3x -4y -5z)
( ) { }
( ) { }
( ) { }
Page 4
We have:
4x
2
-9y
2
= (2x)
2
-(3y)
2
= (2x +3y)(2x -3y)
? 4x
2
-9y
2
= (2x +3y)(2x -3y)
Q u e s t i o n : 3 3
Factorise:
16a
2
- 225b
2
S o l u t i o n :
We have:
16a
2
-225b
2
= (4a)
2
-(15b)
2
= (4a +15b)(4a -15b)
? 16a
2
-225b
2
= (4a +15b)(4a -15b)
Q u e s t i o n : 3 4
Factorise:
9a
2
b
2
- 25
S o l u t i o n :
We have:
9a
2
b
2
-25 = (3ab)
2
-(5)
2
= (3ab +5)(3ab -5)
? 9a
2
b
2
-25 = (3ab +5)(3ab -5)
Q u e s t i o n : 3 5
Factorise:
16a
2
- 144
S o l u t i o n :
We have:
16a
2
-144 = (4a)
2
-(12)
2
= (4a +12)(4a -12) = 4 a + 3 4 a -3 = 16 a +3 a -3
? 16a
2
-144 = 16(a +3)(a -3)
Q u e s t i o n : 3 6
Factorise:
63a
2
- 112b
2
S o l u t i o n :
We have:
63a
2
-112b
2
= 7 9a
2
-16b
2
= 7 (3a)
2
-(4b)
2
= 7(3a +4b)(3a -4b)
? 63a
2
-112b
2
= 7(3a +4b)(3a -4b)
Q u e s t i o n : 3 7
Factorise:
20a
2
- 45b
2
S o l u t i o n :
We have:
20a
2
-45b
2
= 5 4a
2
-9b
2
= 5 (2a)
2
-(3b)
2
= 5(2a +3b)(2a -3b)
? 20a
2
-45b
2
= 5(2a +3b)(2a -3b)
Q u e s t i o n : 3 8
Factorise:
12x
2
- 27
S o l u t i o n :
We have:
12x
2
-27 = 3 4x
2
-9 = 3 (2x)
2
-(3)
2
= 3(2x +3)(2x -3)
? 12x
2
-27 = 3(2x +3)(2x -3)
Q u e s t i o n : 3 9
Factorise:
x
3
- 64x
S o l u t i o n :
We have:
x
3
-64x = x x
2
-64 = x (x)
2
-(8)
2
= x(x +8)(x -8)
? x
3
-64x = x(x +8)(x -8)
Q u e s t i o n : 4 0
Factorise:
16x
5
- 144x
3
S o l u t i o n :
We have:
16x
5
-144x
3
= 16x
3
x
2
-9 = 16x
3
(x)
2
-(3)
2
= 16x
3
(x +3)(x -3)
? 16x
5
-144x
3
= 16x
3
(x +3)(x -3)
Q u e s t i o n : 4 1
( ) ( ) ( ) ( )
( ) { }
( ) { }
( ) { }
( ) { }
( ) { }
Factorise:
3x
5
- 48x
3
S o l u t i o n :
We have:
3x
5
-48x
3
= 3x
3
x
2
-16 = 3x
3
(x)
2
-(4)
2
= 3x
3
(x +4)(x -4)
? 3x
5
-48x
3
= 3x
3
(x +4)(x -4)
Q u e s t i o n : 4 2
Factorise:
16p
3
- 4p
S o l u t i o n :
We have:
16p
3
-4p = 4p 4p
2
-1 = 4p (2p)
2
-(1)
2
= 4p(2p +1)(2p -1)
? 16p
3
-4p = 4p(2p +1)(2p -1)
Q u e s t i o n : 4 3
Factorise:
63a
2
b
2
- 7
S o l u t i o n :
We have:
63a
2
b
2
-7 = 7 9a
2
b
2
-1 = 7 (3ab)
2
-(1)
2
= 7(3ab +1)(3ab -1)
? 63a
2
b
2
-7 = 7(3ab +1)(3ab -1)
Q u e s t i o n : 4 4
Factorise:
1 - b -c
2
S o l u t i o n :
We have:
1 -(b -c)
2
= (1)
2
-(b -c)
2
= {1 +(b -c)}{1 -(b -c)} = (1 +b -c)(1 -b +c)
? 1 -(b -c)
2
= (1 +b -c)(1 -b +c)
Q u e s t i o n : 4 5
Factorise:
(2a + 3b)
2
- 16c
2
S o l u t i o n :
We have:
(2a +3b)
2
-16c
2
= (2a +3b)
2
-(4c)
2
= {(2a +3b)+4c}{(2a +3b)-4c} = (2a +3b +4c)(2a +3b -4c)
? (2a +3b)
2
-16c
2
= (2a +3b +4c)(2a +3b -4c)
Q u e s t i o n : 4 6
Factorise:
(l + m)
2
- (l - m)
2
S o l u t i o n :
We have:
(l +m)
2
-(l -m)
2
= {(l +m)+(l -m)}{(l +m)-(l -m)} = (l +m +l -m)(l +m -l +m) = (2l)(2m)
? (l +m)
2
-(l -m)
2
= (2l)(2m)
Q u e s t i o n : 4 7
Factorise:
(2x + 5y)
2
- 1
S o l u t i o n :
We have:
(2x +5y)
2
-1 = (2x +5y)
2
-(1)
2
= {(2x +5y)+1}{(2x +5y)-1} = (2x +5y +1)(2x +5y -1)
? (2x +5y)
2
-1 = (2x +5y +1)(2x +5y -1)
Q u e s t i o n : 4 8
Factorise:
36c
2
- (5a + b)
2
S o l u t i o n :
We have:
36c
2
-(5a +b)
2
= (6c)
2
-(5a +b)
2
= {(6c)+(5a +b)}{(6c)-(5a +b)} = (6c +5a +b)(6c -5a -b)
? 36c
2
-(5a +b)
2
= (6c +5a +b)(6c -5a -b)
Q u e s t i o n : 4 9
Factorise:
(3x - 4y)
2
- 25z
2
S o l u t i o n :
We have:
(3x -4y)
2
-25z
2
= (3x -4y)
2
-(5z)
2
= {(3x -4y)+5z}{(3x -4y)-5z} = (3x -4y +5z)(3x -4y -5z)
? (3x -4y)
2
-25z
2
= (3x -4y +5z)(3x -4y -5z)
( ) { }
( ) { }
( ) { }
Q u e s t i o n : 5 0
Factorise:
x
2
- y
2
- 2y - 1
S o l u t i o n :
We have:
x
2
-y
2
-2y -1 = x
2
- y
2
+2y +1
= (x)
2
-(y +1)
2
= {x +(y +1)}{x -(y +1)} = (x +y +1)(x -y -1)
? x
2
-y
2
-2y -1 = (x +y +1)(x -y -1)
Q u e s t i o n : 5 1
Factorise:
25 - a
2
- b
2
- 2ab
S o l u t i o n :
We have:
25 -a
2
-b
2
-2ab = 25 - a
2
+b
2
+2ab
= 25 -(a +b)
2
= (5)
2
-(a +b)
2
= {5 +(a +b)}{5 -(a +b)} = (5 +a +b)(5 -a -b)
? 25 -a
2
-b
2
-2ab = (5 +a +b)(5 -a -b)
Q u e s t i o n : 5 2
Factorise:
25a
2
- 4b
2
+ 28bc - 49c
2
S o l u t i o n :
We have:
25a
2
-4b
2
+28bc -49c
2
= 25a
2
- 4b
2
-28bc +49c
2
= (5a)
2
-(2b -7c)
2
= {5a +(2b -7c)}{5a -(2b -7c)} = (5a +2b -7c)(5a -2b +7c)
? 25a
2
-4b
2
+28bc -49c
2
= (5a +2b -7c)(5a -2b +7c)
Q u e s t i o n : 5 3
Factorise:
9a
2
- b
2
+ 4b - 4
S o l u t i o n :
We have:
9a
2
-b
2
+4b -4 = 9a
2
- b
2
-4b +4
= (3a)
2
-(b -2)
2
= {3a +(b -2)}{3a -(b -2)} = (3a +b -2)(3a -b +2)
? 9a
2
-b
2
+4b -4 = (3a +b -2)(3a -b +2)
Q u e s t i o n : 5 4
Factorise:
100 - (x - 5)
2
S o l u t i o n :
We have:
100 -(x -5)
2
= (10)
2
-(x -5)
2
= {10 +(x -5)}{10 -(x -5)} = (10 +x -5)(10 -x +5) = (5 +x)(15 -x)
? 100 -(x -5)
2
= (5 +x)(15 -x)
Q u e s t i o n : 5 5
Factorise:
Evaluate {405
2
- 395
2
}.
S o l u t i o n :
We have:
(405)
2
-(395)
2
= (405 +395)(405 -395) = (800 ×10) = 8000
? (405)
2
-(395)
2
= 8000
Q u e s t i o n : 5 6
Factorise:
Evaluate {7.8
2
- 2.2
2
}.
S o l u t i o n :
We have:
(7. 8)
2
-(2. 2)
2
= (7. 8 +2. 2)(7. 8 -2. 2) = (10 ×5. 6) = 56
? (7. 8)
2
-(2. 2)
2
= 56
( )
( )
( )
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{ }
{ }
{ }
{ }
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Full syllabus notes, lecture & questions for RS Aggarwal Solutions: Exercise 7B - Factorisation | Mathematics (Maths) Class 8 - Class 8 | Plus excerises question with solution to help you revise complete syllabus for Mathematics (Maths) Class 8 | Best notes, free PDF download
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Additional Information about RS Aggarwal Solutions: Exercise 7B - Factorisation for Class 8 Preparation
RS Aggarwal Solutions: Exercise 7B - Factorisation Free PDF Download
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RS Aggarwal Solutions: Exercise 7B - Factorisation Notes
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RS Aggarwal Solutions: Exercise 7B - Factorisation Class 8 Questions
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The content of RS Aggarwal Solutions: Exercise 7B - Factorisation is prepared as per the latest Class 8 syllabus.
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