Class 8 Exam > Class 8 Notes > Mathematics (Maths) Class 8 > RS Aggarwal Solutions: Exercise 7B - Factorisation
RS Aggarwal Solutions: Exercise 7B - Factorisation | Mathematics (Maths) Class 8 PDF Download
| Download, print and study this document offline |
Please wait while the PDF view is loading
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
( )
( )
( )
( )
{ }
{ }
{ }
{ }
Read More
|
79 videos|408 docs|31 tests
|
Related Exams
About this Document
|
4.98/5 Rating |
|
Nov 21, 2024 Last updated |
Document Description: RS Aggarwal Solutions: Exercise 7B - Factorisation for Class 8 2024 is part of Mathematics (Maths) Class 8 preparation.
The notes and questions for RS Aggarwal Solutions: Exercise 7B - Factorisation have been prepared according to the Class 8 exam syllabus. Information about RS Aggarwal Solutions: Exercise 7B - Factorisation covers topics
like and RS Aggarwal Solutions: Exercise 7B - Factorisation Example, for Class 8 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for RS Aggarwal Solutions: Exercise 7B - Factorisation.
Introduction of RS Aggarwal Solutions: Exercise 7B - Factorisation in English is available as part of our Mathematics (Maths) Class 8
for Class 8 & RS Aggarwal Solutions: Exercise 7B - Factorisation in Hindi for Mathematics (Maths) Class 8 course.
Download more important topics related with notes, lectures and mock test series for Class 8
Exam by signing up for free. Class 8: RS Aggarwal Solutions: Exercise 7B - Factorisation | Mathematics (Maths) Class 8
Description
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
Information about RS Aggarwal Solutions: Exercise 7B - Factorisation
In this doc you can find the meaning of RS Aggarwal Solutions: Exercise 7B - Factorisation defined & explained in the simplest way possible. Besides explaining types of
RS Aggarwal Solutions: Exercise 7B - Factorisation theory, EduRev gives you an ample number of questions to practice RS Aggarwal Solutions: Exercise 7B - Factorisation tests, examples and also practice Class 8
tests
|
Explore Courses for Class 8 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
Extra Questions
,past year papers
,Exam
,Semester Notes
,Previous Year Questions with Solutions
,Summary
,shortcuts and tricks
,Viva Questions
,RS Aggarwal Solutions: Exercise 7B - Factorisation | Mathematics (Maths) Class 8
,study material
,video lectures
,Objective type Questions
,practice quizzes
,Free
,MCQs
,Important questions
,ppt
,mock tests for examination
,RS Aggarwal Solutions: Exercise 7B - Factorisation | Mathematics (Maths) Class 8
,RS Aggarwal Solutions: Exercise 7B - Factorisation | Mathematics (Maths) Class 8
,Sample Paper
;
Additional Information about RS Aggarwal Solutions: Exercise 7B - Factorisation for Class 8 Preparation
RS Aggarwal Solutions: Exercise 7B - Factorisation Free PDF Download
The RS Aggarwal Solutions: Exercise 7B - Factorisation is an invaluable resource that delves deep into the core of the Class 8 exam.
These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
With the help of these notes, you can grasp complex subjects quickly, revise important points easily,
and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner,
allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material,
or toppers' notes, this PDF has got you covered. Download the RS Aggarwal Solutions: Exercise 7B - Factorisation now and kickstart your journey towards success in the Class 8 exam.
Importance of RS Aggarwal Solutions: Exercise 7B - Factorisation
The importance of RS Aggarwal Solutions: Exercise 7B - Factorisation cannot be overstated, especially for Class 8 aspirants.
This document holds the key to success in the Class 8 exam.
It offers a detailed understanding of the concept, providing invaluable insights into the topic.
By knowing the concepts well in advance, students can plan their preparation effectively.
Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.
RS Aggarwal Solutions: Exercise 7B - Factorisation Notes
RS Aggarwal Solutions: Exercise 7B - Factorisation Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to RS Aggarwal Solutions: Exercise 7B - Factorisation.
It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation.
Practice papers and question papers enable you to assess your progress effectively.
Additionally, the paper analysis provides valuable tips for tackling the exam strategically.
Access to Toppers' notes gives you an edge in understanding complex concepts.
Whether you're a beginner or aiming for advanced proficiency, RS Aggarwal Solutions: Exercise 7B - Factorisation Notes on EduRev are your ultimate resource for success.
RS Aggarwal Solutions: Exercise 7B - Factorisation Class 8 Questions
The "RS Aggarwal Solutions: Exercise 7B - Factorisation Class 8 Questions" guide is a valuable resource for all aspiring students preparing for the
Class 8 exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study RS Aggarwal Solutions: Exercise 7B - Factorisation on the App
Students of Class 8 can study RS Aggarwal Solutions: Exercise 7B - Factorisation alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the RS Aggarwal Solutions: Exercise 7B - Factorisation,
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 7B - Factorisation is prepared as per the latest Class 8 syllabus.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up
within 7 days!
within 7 days!
Takes less than 10 seconds to signup