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Class 8 RD Sharma Solutions – Chapter 7 Factorization-Exercise 7.5 | Set 2
  • Last Updated : 24 Nov, 2020

Factorize each of the following expressions:

Question 24. 50/x2 – 2x2/81

Solution:

50/x2 – 2x2/81

= 2(25/x2 – x2/81)

= 2[(5/x)2 – (x/9)2]

= 2(5/x – x/9) (5/x + x/9)



Question 25. 256x5 – 81x

Solution:

256x5 – 81x

= x(256x4 – 81)

= x[(16x2)2 – (9)2]

= x(16x2 – 9) (16x2 + 9)

Question 26. a4 – (2b + c)4

Solution:

a4 – (2b + c)4

= (a2)2 – [(2b + c)2]2



= [a2 – (2b + c)2] [a2 + (2b + c)2]

= [a + (2b + c)] [a – (2b + c)] [a2 + (2b + c)2]

= (a + 2b + c) (a – 2b – c) [a2 + (2b + c)2]

Question 27. (3x + 4y)4 – x4

Solution:

(3x + 4y)4 – x4

= [(3x + 4y)2]2 – (x2)2

= [(3x + 4y)2 – x2] [(3x + 4y)2 + x2]

= [(3x + 4y) – x] [(3x + 4y) + x] [(3x + 4y)2 + x2]

= (2x + 4y) (4x + 4y) [(3x + 4y)2 + x2]

= 8(x + 2y) (x + y) [(3x + 4y)2 + x2]

Question 28. p2q2 – p4q4

Solution:

p2q2 – p4q4

= p2q2 (1 – p2q2)

= p2q2 (1 + pq) (1 – pq)

Question 29. 3x3y – 243xy3

Solution:

3x3y – 243xy3

= 3xy (x2 – 81y2)

= 3xy [x2 – (9y)2]

= 3xy (x – 9y) (x + 9y)

Question 30. a4b4 – 16c4

Solution:

a4b4 – 16c4

= (a2b2)2 – (4c2)2

= (a2b2 – 4c2) (a2b2 + c2)

= [a2b2 – (2c)2] (a2b2 + c2)

= (ab – 2c) (ab + 2c) (a2b2 + c2)

Question 31. x4 – 625

Solution:

x4 – 625

= (x2)2 – (25)2

= (x2 – 25) (x2 + 25)

= (x2 – 52) (x2 + 25)

= (x – 5) (x + 5) (x2 + 25)

Question 32. x4 – 1

Solution:

x4 – 1

= (x2)2 – 12

= (x2 – 1)(x2 +1)

= (x + 1)(x – 1) (x2 + 1)

Question 33. 49(a – b)2 – 25(a + b)2

Solution:

49(a – b)2 – 25(a + b)2

= [7(a – b)]2 – [5 (a + b)]2

= [7(a – b) – 5 (a + b)] [7(a – b) + 5 (a + b)]

= (7a – 7b -5a – 5b) (7a – 7b + 5a + 5b)

= (2a – 12b) (12a – 2b)

= 4(a – 6b)(6a – b)

Question 34. x – y – x2 + y2

Solution:

x – y – x2 + y2

= (x – y) – (x2 – y2)

= (x – y) – (x  – y)(x + y)

= (x – y) [1 – (x + y)]

= (x – y) (1 – x – y)

Question 35. 16(2x – 1)2 – 25y2

Solution:

16(2x – 1)2 – 25y2

= [4(2x – 1)]2 – (5y)2

= [4(2x – 1) – 5y] [4(2x – 1) + 5y]

= (8x – 4 – 5y) ( 8x – 4 + 5y)

Question 36. 4(xy + 1)2 – 9(x – 1)2

Solution:

4(xy + 1)2 – 9( x- 1)2

= [2(xy + 1)]2 – [3(x – 1)]2

= [2(xy + 1) – 3(x – 1)] [2(xy + 1) + 3(x – 1)]

= (2xy + 2 – 3x + 3) (2xy + 2 + 3x – 3)

= (2xy – 3x + 5) (2xy + 3x – 1)

Question 37. (2x + 1)2 – 9x4

Solution:

(2x + 1)2 – 9x4

= (2x + 1)2 – (3x2 )2

= [(2x +1) – 3x2] [(2x + 1) + 3x2]

= (-3x2 + 2x + 1)(3x2 + 2x + 1)

= (-3x2 + 3x – x + 1) (3x2 + 2x + 1)

= [3x(1 – x) + (1 – x)] (3x2 + 2x + 1)

= (3x +1) (1 – x) (3x2 + 2x + 1)

Question 38. x4 – (2y – 3z)2

Solution:

x4 – (2y – 3z)2

= (x2)2 – (2y – 3z)2

= [x2 – (2y – 3z)] [x2 + (2y – 3z)]

= (x2 – 2y + 3z) (x2 + 2y – 3z)

Question 39. a2 – b2 + a – b

Solution:

a2 – b2 + a – b

= (a2 – b2) + (a – b)

= [(a – b) (a + b)] + (a – b)

= (a – b) (a + b + 1)

Question 40. 16a4 – b4

Solution:

16a4 – b4

= (4a2)2 – (b2)2

= (4a2 – b2) (4a2 + b2)

= [(2a)2 – b2] (4a2+ b2)

= (2a – b) (2a + b) (4a2 + b2)

Question 41. a4 – 16(b – c)4

Solution:

a4 – 16(b – c)4

= (a2)2 – [4(b – c)2]2

= [a2 – 4(b – c)2] [a2 + 4(b – c)2]

= {a2 – [2(b – c)]2}[a2 + 4(b – c)2]

= [a – 2(b – c)] [a + 2(b – c)] [a2 + 4(b – c)2]

= (a – 2b + 2c) (a + 2b – 2c) [a2 + 4(b – c)2]

Question 42. 2a5 – 32a

Solution:

2a5 – 32a

= 2a(a5 – 1 )

= 2a [ (a2)2 – 12 ]

= 2a ( a2 – 1) (a2+ 1)

= 2a (a+1) (a-1) (a2+1)

Question 43. a4b4 – 81c4

Solution:

Answer:

   a4b4 – 81c4

= (a2b2)2 – (9c2)2

= (a2b2 – 9c2) (a2b2 + 9c2)

= [(ab)2 – (3c)2 ] (a2b2 + 9c2)

= (ab – 3c) (ab + 3c) (a2b2 + 9c2)

Question 44. xy9 – x9y

Solution:

xy9 – x9y

= xy(y8 – x8)

= xy [(y4)2 – (x4)2]

= xy (y4 – x4)(y4 + x4)

= xy [(y2)2 – (x2)2] (y4 + x4)

= xy [(y2 – x2)(y2 + x2)(y4 + x4)

= xy (y – x) (y + x) (y2 + x2) (y4 + x4)

Question 45. x3 – x

Solution:

x3 – x

= x(x2 – 1)

= x (x + 1)(x – 1)

Question 46. 18a2x2 – 32

Solution:

18a2x2 – 32

= 2(9a2x2 – 16)

= 2[(3ax)2 – 42]

= 2(3ax – 4) (3ax + 4)

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