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Class 8 RD Sharma Solutions- Chapter 7 Factorization – Exercise 7.6
  • Last Updated : 11 Feb, 2021

Question 1) 4x2 + 12xy + 9y2

Solution:

(2x)2 + 2 × 2x × 3y + (3y)2

⇒ (2x + 3y)2                        [(a + b)2 = a2 + b2 + 2ab]

⇒ (2x + 3y) (2x + 3y)

Question 2) 9a2 – 24ab + 16b2

Solution:



(3a)2 – 2 × 3a × 4b + (4b)2

⇒ (3a – 4b)2                               [(a + b)2 = a2 + b2 + 2ab]

⇒ (3a – 4b) (3a – 4b)

Question 3) p2q2 – 6pqr + 9r

Solution:

(pq)2 – 2 x pq x 3r + (3r)2

⇒ (pq – 3r)2                                 [(a + b)2 = a2 + b2 + 2ab]

⇒ (pq -3r) (pq -3r)    

Question 4) 36a2 + 36a + 9

Solution:



9(4a2 + 4a + 1)

⇒ 9{(2a)2 + 2 × 2a × 1 + (1)2

⇒ 9(2a + 1)2                                  [(a + b)2 = a2 + b2 + 2ab]

⇒ 9 (2a + 1)(2a + 1)

Question 5) a2 + 2ab + b2 – 16

Solution:

a2 + 2ab + b2 – 16

⇒ (a + b)2 – (4)2   

⇒ (a + b + 4) (a + b – 4)

Question 6) 9z2 – x2 + 4xy – 4y2

Solution:

9z2 – x2 + 4xy – 4y2

⇒ 9z2 – (x2 – 4xy + 4y2)

⇒ 9z2 – (x2 – 2x × 2y + (2y)2)                   [(a + b)2 = a2 + b2 + 2ab]

⇒ 9z2 – (x – 2y)2

⇒ (3z)2 – (x – 2y)2

⇒ (3z – (x – 2y)) (3z + (x – 2y))

⇒ (3z – x + 2y) (3z + x – 2y)

Question 7) 9a4 – 24 a2b2 + 16b4 – 256

Solution:

9a4 – 24 a2b2 + 16b4 – 256

⇒ (9a4 – 24a2b2 + 16b4 ) – 256

⇒ [(3a2)2 – 2 × 3a2 × 4b2] – 256                          

⇒ (3a2 – 4b2)2 – (16)2

⇒ (3a2 – 4b2 – 16)(3a2 – 4b2 + 16)

Question 8) 16 – a6 + 4a3b3 – 4b6

Solution:

16 – (a6 – 4a3b3 + 4b6)

⇒ 16 – [(a3)2 – 2 × a3 × 2b3 + (2b3)2]

⇒ 16 – (a3– 2b3)2

⇒ (4)2 – (a3 – 2b3)2

⇒ (4 – a3 + 2b3)(4 + a3 – 2b3)

Question 9) a2 – 2ab + b2 – c2

Solution:

(a2 – 2ab + b2) – c2

⇒ (a2 – 2 × a × b + b2) – c2

⇒ (a – b)2 – c2

⇒ (a – b – c) (a – b + c)

Question 10) X2 + 2X + 1 – 9Y2

Solution:

X2 + 2X + 1 – 9Y2

⇒ (X2 + 2 × X × 1 + 12 ) – 9Y2

⇒ (X + 1)2 – (3Y)2

⇒ (X + 1 – 3Y) (X + 1 + 3Y)

Question 11) a2 + 4ab + 3b2

Solution:

a2 + 4ab + 4b2 – b2

⇒ (a2+ 2 × 2b × a + (2b)2) – b2

⇒ (a + 2b)2 – b2

⇒ (a + 2b – b) (a + 2b+ b)

⇒ (a + b) (a + 3b)

Question 12) 96 – 4x – x2

Solution:

100-4 -4x -x2

⇒ 100 – (x2 + 4x + 4)

⇒ (10)2 – (x + 2)2

⇒ (10 – x – 2) (10 + x + 2)

⇒ (8 – x) (12 + x)

Question 13) a4 + 3a2 + 4

Solution: 

a4 + 4a2 – a2 + 4

⇒ [(a2)2 + 2 × 2 × a2 + (2)2] – a2

⇒ (a2 + 2)2 – a2

⇒ (a2 + 2 – a) (a2 + 2 + a)

Question 14) 4x4 + 1

Solution:

4x4 + 4x2 + 1 – 4x2

⇒ [(2x2)2 + 2 × 2x2 × 1 + (1)2] – (2x)2

⇒ (2x2 +1)2 – (2x)2

⇒ (2x2 + 1 – 2x) (2x2 + 1 + 2x)

Question 15) 4x4+ y4

Solution:

4x4 + 4x2y2 + y4 – 4x2y2

⇒ [(2x2)2+ 2 × 2x2 × y2 + (y2)2] – 4x2y2

⇒ (2x2 + y2)2 – (2xy)2

⇒ (2x2 + y2 – 2xy) (2x2 + y2 + 2xy)

Question 16) (x + 2)2 – 6(x + 2) + 9

Solution:

(x + 2)2 – 6(x + 2) + 9

⇒ (x + 2)2 -2 × (x + 2) × 3 + (3)

⇒ (x + 2 – 3)2

⇒ (x – 1)2

⇒ (x – 1) (x – 1)

Question 17) 25 – p2 – q2 – 2pq

Solution:

25 – (p2 + q2 + 2pq)

⇒ (5)2 – (p + q)2

⇒ (5 – p – q) (5 + p + q)

Question 18) x2 + 9y2 – 6xy – 25a2

Solution:

(x2 – 6xy + 9y2) – 25a2

⇒ (x – 3y)2 – 25a2

⇒ (x – 3y – 5a) (x – 3y + 5a)

Question 19) 49 – a2 + 8ab – 16b2

Solution:

49 – (a2 – 8ab + 16b2)

⇒ (7)2 – (a- 4b)2

⇒ (7 – a – 4b) (7 + a + 4b)

Question 20) a2 – 8ab + 16b2 – 25c2

Solution:

a2 – 8ab +16b2 – 25c2

⇒ (a2 – 8ab + 16b2) – 25c2

⇒ (a – 4b)2 – (5c)2

⇒ (a – 4b – 5c) (a – 4b + 5c)

Question 21) x2 – y2 + 6y – 9

Solution:

x2 – (y2 – 6y + 9)

⇒ x2 – (y – 3)2

⇒ (x – y + 3) (x + y – 3)

Question 22) 25x2 – 10x + 1 – 36y2

Solution:

25x2 – 10x + 1 – 36y2

⇒ [(5x)2 – 2 × 5x × 1 + 12] – 36y2

⇒ (5x – 1)2 – (6y)2

⇒ (5x – 1 – 6y) (5x – 1 + 6y)

Question 23) a2 – b2 + 2bc – c2

Solution:

a2 – b2 + 2bc – c2

⇒ a2 – (b2 – 2bc + c2)

⇒ a2 – (b – c )2

⇒ (a – b + c) (a + b – c)

Question 24) a2 + 2ab + b2 – c2

Solution:

a2 + 2ab + b2 – c2

⇒ (a + b)2 – c2

⇒ (a + b – c) (a + b + c)

Question 25) 49 – x2– y2 + 2xy

Solution:

49 – x2 – y2 + 2xy

⇒ 49 – (x2 + y2 – 2xy)

⇒ (7 – x + y) (7 + x – y)

Question 26) a2 + 4b2 – 4ab – 4c2

Solution:

a2 + 4b2 – 4 ab – 4c2

⇒ (a – 2b)2 – (2c)2

⇒ (a – 2b – 2c) (a – 2b + 2c)

Question 27) x2 – y2 – 4xz + 4z2

Solution:

x2 – y2 – 4xz + 4z2

⇒ (x – 2z)2 – y2

⇒ (x – 2z – y)(x – 2z + y)

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