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Class 8 RD Sharma Solutions – Chapter 7 Factorization – Exercise 7.5 | Set 1

Last Updated : 07 Apr, 2021
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Factorize each of the following expressions:

Question 1. 16x2 – 25y2

Solution:

16x2 – 25y2 

= (4x)2 – (5y)2 

= (4x – 5y)(4x + 5y)  

Question 2. 27x2 – 12y2

Solution:

27x2 – 12y2

= 3(9x2 – 4y2)

= 3[(3x)2 – (2y)2]

= 3(3x – 2y)(3x + 2y) 

Question 3. 144a2 – 289b2

Solution:

144a2 – 289b2

= (12a)2 – (17b)2 

= (12a – 17b)(12a + 17b) 

Question 4. 12m2 – 27

Solution:

12m2 – 27

= 3(4m2 – 9) 

= 3[(2m)2 – 32

= 3(2m – 3)(2m + 3) 

Question 5. 125x2 – 45y2

Solution:

125x2 – 45y2

= 5(25x2 – 9y2

= 5[(5x)2 – (3y)2

= 5(5x – 3y)(5x + 3y) 

Question 6. 144a2 – 169b2

Solution:

144a2 – 169b2

= (12a)2 – (13b)2 

= (12a – 13b)(12a + 13b)

Question 7. (2a – b)2 – 16c2

Solution:

(2a – b)2 – 16c2

= (2a – b)2 – (4c)2 

= [(2a – b) + 4c][(2a – b) – 4c] 

= (2a – b + 4c)(2a – b – 4c) 

Question 8. (x + 2y)2 – 4(2x – y)2

Solution:

(x + 2y)2 – 4(2x – y)2

= (x + 2y)2 – [2(2x – y)]2 

= [(x + 2y) – 2(2x – y)][(x + 2y) + 2(2x – y)] 

= (x + 2y – 4x + 2y)(x + 2y + 4x – 2y) 

= 5x(4y – 3x) 

Question 9. 3a5 – 48a3

Solution:

3a5 – 48a3

= 3a3(a2 – 16) 

= 3a3(a2 – (4)2

= 3a3(a – 4)(a + 4) 

Question 10. a4 – 16b4

Solution:

a4 – 16b4  

= a4 – 24b4 

= (a2)2 – (22b2)2

= (a2 – 22b2)(a2 + 22b2

= [a2 – (2b)2](a2 + 4b2

= [a2 – (2b)2](a2 + 4b2

= (a – 2b)(a + 2b)(a2 + 4b2

Question 11. x8 – 1

Solution:

x8 – 1

= (x4)2 – 12

= [(x2)2 – 12](x4 + 1)

= [(x2 – 1)(x2 + 1)](x4 + 1)

= (x – 1)(x + 1)(x2 + 1)(x4 + 1) 

Question 12. 64 – (a + 1)2

Solution:

64 – (a + 1)2

= (8)2 – (a + 1)2

= [8 – (a + 1)][8 + (a + 1)]  

= (8 – a – 1)(8 + a + 1)  

= (7-a)(9+a)  

Question 13. 36L2 – (m + n)2

Solution:

36L2 – (m + n)2

= (6L)2 – (m + n)2

= [6L – (m + n)][6L + (m + n)]  

= (6L – m – n)(6L + m + n)  

Question 14. 25x4y4 – 1

Solution:

25x4y4 – 1

= (5x2y2)2 – 12

= (5x2y2 – 1)(5x2y2 + 1)  

Question 15. a4 – 1/b4

Solution:

a4 – 1/b4

= (a2)2 – (1/b2)2

= (a2 – 1/b2)(a2 + 1/b2)  

= (a – 1/b)(a + 1/b)(a2 + 1/b2)  

Question 16. x3 – 144x

Solution:

x3 – 144x

= x(x2 – 144)  

= x(x2 – 122)  

= x(x – 12)(x + 12)  

Question 17. (x – 4y)2 – 625

Solution:

(x – 4y)2 – 625  

= (x – 4y)2 – 252  

= [(x – 4y) – 25] [(x – 4y) + 25]  

= (x – 4y – 25)(x – 4y + 25)

Question 18. 9(a – b)2 – 100(x – y)2

Solution:

9(a – b)2 – 100(x – y)2

= [3(a – b)]2 – [10 (x – y)]2

= [3(a – b) -10(x – y)] [3(a – b) + 10(x – y)]

= (3a – 3b – 10x + 10y) (3a – 3b + 10x – 10y)

Question 19. (3 + 2a)2 – 25a2

Solution:

(3 + 2a)2 – 25a2

= (3 + 2a)2 – (5a)2

= (3 + 2a + 5a)(3 + 2a – 5a)

= (3 + 7a)(3 – 3a)

Question 20. (x + y)2 – (a – b)2

Solution:

(x + y)2 – (a – b)2

= [(x + y) + (a – b)] [(x + y) – (a – b)]

= (x + y + a – b) (x + y – a + b)

Question 21. 1/16 x2y2 – 4/49y2z2

Solution:

1/16 x2y2 – 4/49y2z2

= (1/4xy)2 – (2/7 yz)2

= (1/4xy – 2/7yz) (1/4xy + 2/7yz)

= [y (1/4x – 2/7z)] [y(1/4x + 2/7z)]

= y2 (1/4x – 2/7z) (1/4x + 2/7z)

Question 22. 75a3b2 – 108ab4

Solution:

75a3b2 – 108ab4

= 3ab2(25a2 – 36b2)

= 3ab2[(5a)2 – (6b)2]

= 3ab2[(5a – 6b)(5a + 6b)]

= 3ab2(5a – 6b)(5a + 6b)

Question 23. x5 – 16x3

Solution:

x5 – 16x3

= x3(x2 – 16)

= x3(x2 – 42)

= x3(x – 4)(x + 4)

Chapter 7 Factorization – Exercise 7.5 | Set 2



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