RD Sharma Solutions for Class 8 Math Chapter 7 - Factorization (Part-2) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Mathematics

Created by: Abhishek Kapoor

Class 8 : RD Sharma Solutions for Class 8 Math Chapter 7 - Factorization (Part-2) Class 8 Notes | EduRev

The document RD Sharma Solutions for Class 8 Math Chapter 7 - Factorization (Part-2) Class 8 Notes | EduRev is a part of the Class 8 Course RD Sharma Solutions for Class 8 Mathematics.
All you need of Class 8 at this link: Class 8

Question 1: Factorize the following:
3x − 9

Answer 1: The greatest common factor of the terms 3x and -9 of the expression 3x - 9 is 3. 
Now.
3x = 3x
and
-9 = 3.-3
Hence, the expression 3x - 9 can be factorised as 3(x - 3). 

Question 2: Factorize the following:
5x − 15x2

Answer 2: The greatest common factor of the terms 5x and 15x2 of the expression 5x - 15x2 is 5x. 
Now,
5x = 5x ×× 1 
and
-15x2 = 5x ×× -3x
Hence, the expression 5x - 15x2 can be factorised as 5x(1 - 3x). 

Question 3: Factorize the following:
20a12b2 − 15a8b4

Answer 3: The greatest common factor of the terms 20a12b2 and -15a8b4 of the expression 20a12b2 - 15a8b4 is 5a8b2.
20a12b2 = 5×4×a8×a4×b2 = 5a8×b2××4a4 and -15a8b4 = 5×-3×a8×b2×b2 = 5a8b2 ×× -3b2
Hence, the expression 20a12b2 - 15a8b4 can be factorised as 5a8b2(4a4-3b2) 

Question 4: Factorize the following:
72x6y7 − 96x7y6

Answer 4: The greatest common factor of the terms 72x6y7 and -96x7y6 of the expression 72x6y7 - 96x7y64 is 24x6y6.
Now,
72x6y7 = 24x6y6 ×× 3y
and 
-96x7y6 = 24x6y6 ×× -4x
Hence, the expression 72x6y7 - 96x7y6 can be factorised as 24x6y6(3y - 4x). 

Question 5: Factorize the following:
20x3 − 40x2 + 80x

Answer 5: The greatest common factor of the terms 20x3, -40x2 and 80x of the expression 20x3 - 40x2 + 80x is 20x.
Now,
20x3 = 20x ×× x2
-40x2 = 20x ×× -2x
and
80x = 20x ×× 4
Hence, the expression 20x3 - 40x2 + 80x can be factorised as 20x(x2 - 2x + 4). 
Question 6: Factorize the following:
2x3y2 − 4x2y3 + 8xy4

Answer 6: The greatest common factor of the terms 2x3y2, -4x2y3 and 8xy4 of the expression 2x3y2 - 4x2y3+ 8xy4y64 is 2xy2. 
Now,
2x3y2 = 2xy2  ×× x2  
-4x2y3 = 2xy2 ×× -2xy
8xy4 = 2xy×× 4y2
Hence, the expression 2x3y2 - 4x2y3 + 8xy4 can be factorised as 2xy2(x2 - 2xy + 4y2). 

Question 7: Factorize the following:
10m3n2 + 15m4n − 20m2n3

Answer 7: The greatest common factor of the terms 10m3n2, 15m4n and -20m2n3 of the expression 10m3n2 + 15m4n - 20m2n3 is 5m2n.
Now,
10m3n= 5m2×× 2mn
15m4n = 5m2×× 3m2
-20m2n= 5m2×× -4n2
Hence, 10m3n2 + 15m2n - 20m2n3 can be factorised as 5m2n(2mn + 3m2 - 4n2). 

Question 8: Factorize the following:
2a4b4 − 3a3b5 + 4a2b5

Answer 8: The greatest common factor of the terms 2a4b4, -3a3b5 and 4a2b5 of the expression 2a4b4 - 3a3b5 + 4a2b5 is a2b4.
Now,
2a4b= a2b×× 2a2
-3a3b= a2b4 ×× -3ab 
4a2b= a2b4 ×× 4b
Hence, (2a4b4 - 3a3b5 + 4a2b5) can be factorised as [a2b4(2a2 - 3ab + 4b)]. 

Question 9: Factorize the following:
28a2 + 14a2b2 − 21a4

Answer 9: The greatest common factor of the terms 28a2, 14a2b2 and 21
a4 of the expression 28a2+14a2b221a4 is 7a2. 
Also, we can write 28a2=7a2×4, 14a2b2=7a2×2b2 and 21a4=7a2×3a2. 
 28a2+14a2b221a4=7a2×4+7a2×2b27a2×3a2 
= 7a2(4+2b23a2) 
Question 10: Factorize the following:
a4b − 3a2b2 − 6ab3 

Answer 10: The grea