## RS Aggarwal Class 8 Solutions Chapter 7 Factorisation Ex 7B

These Solutions are part of RS Aggarwal Solutions Class 8. Here we have given RS Aggarwal Solutions Class 8 Chapter 7 Factorisation Ex 7B.

Other Exercises

Question 1.
Solution:
x2 – 36
= (x)2 – (6)2 { ∵ a2 – b2 = (a + b) (a – b)}
= (x + 6) (x – 6) Ans.

Question 2.
Solution:
4a2 – 9
= (2a)2 – (3)2
= (2a + 3) (2a – 3)
{ ∵ a2 – b2 = (a + b) (a – b)}

Question 3.
Solution:
81 – 49x2
= (9)2 – (7x)2
= (9 + 7x) (9 – 7x) { ∵ a2 – b2 = (a + b) (a – b)}

Question 4.
Solution:
= (2x)2 – (3y)2
= (2x + 3y)(2x-3y)
{∵ a2 – b2 = (a + b) (a – b)}

Question 5.
Solution:
Using a2 – b2
= (a + b) (a – b)
= 16a2 – 225b2
= (4a)2 – (15b)2
= (4a + 15b) (4b – 5b)

Question 6.
Solution:
Using a2 – b2
= (a + b) (a – b)
= (3ab)2 – (5)2
= (3ab + 5) (3ab – 5)

Question 7.
Solution:
Using a2 – b2 = (a + b) (a – b)
16a2 – 144 = (4a)2 = (12)2
= (4a + 12) (4a – 12)
= 4 (a + 3) x 4 (a – 3)
= 16 (a + 3) (a – 3)

Question 8.
Solution:
63a2 – 112b2
= 7 (9a2 – 16b2)
= 7 [(3a)2 – (4b)2
= 7 (3a + 4b) (3a – 4b)

Question 9.
Solution:
20a2 – 45b2
= 5 {4a2 – 9b2}
= 5{(2a)2 – (3b)2)
= 5(2a + 3b) (2a – 3b) Ans.

Question 10.
Solution:
12x2 – 27
= 3(4x2 – 9)
= 3{(2x)2 – (3)2}
= 3(2x + 3) (2x – 3) Ans.

Question 11.
Solution:
x3 – 64x
= x(x2 – 64)
= x{(x)2 – (8)2}
= x(x + 8) (x – 8) Ans.

Question 12.
Solution:
16x5 – 144x3
= 16x3 [x2 – 9]
= 16x3 [(x)2 – (3)2]
= 16x3 (x + 3) (x – 3)

Question 13.
Solution:
3x5 – 48x3
= 3x3 {x2 – 16}
= 3x3{(x)2 – (4)2}
= 3x3 (x + 4) (x – 4) Ans.

Question 14.
Solution:
16p3 – 4p
= 4p [4p2 – 1]
= 4p ((2p)2 – (1)2]
= 4p(2p + 1)(2p – 1)

Question 15.
Solution:
63a2b2 – 7
= 7(9a2b2 – 1)
= 7{(3ab)2 – (1)2)
= 7(3ab + 1) (3ab – 1) Ans.

Question 16.
Solution:
1 – (b – c)2
= (1)2 – (b – c)2
= (1 + b + c) (1 – b + c) Ans.
{ ∵ a2 – b2 = (a + b) (a – b)}

Question 17.
Solution:
(2a + 3b)2 – 16c2
= (2a + 3b)2 – (4c)2
=(2a + 3b + 4c)(2a + 3b – 4c)Ans.
{ ∵ a2 – b2 = (a + b)(a – b)}

Question 18.
Solution:
(l + m)2 – (l – m)2
= (l + m + l – m)(l + m – l + m)
{ ∵ a2 – b2 = (a + b)(a – b)}
= 2l x 2m = 4lm

Question 19.
Solution:
(2x + 5y)2 – (1)2
=(2x + 5y + 1)(2x + 5y – 1)
{ ∵ a2 – b2 = (a + b)(a – b)}

Question 20.
Solution:
36c2 – (5a + b)2
= (6c)2 – (5a + b)2
{ ∵ a2 – b2 = (a + b)(a – b)}
= (6c + 5a + b)(6c – 5a – b)

Question 21.
Solution:
(3x – 4y)2 – 25z2
= (3x – 4y)2 – (5z)2
= (3x – 4y + 5z) (3x – 4y – 5z) Ans.

Question 22.
Solution:
x2 – y2 – 2y – 1
= x2 – (y2 + 2y + 1)
= (x)2 – (y + 1)2
= (x + y + 1)(x – y – 1)Ans.

Question 23.
Solution:
25 – a2 – b2 – 2ab
= 25 – (a2 + b2 + 2ab)
= (5)2 – (a + b)2
= (5 + a + b)(5 – a – b)Ans.

Question 24.
Solution:
25a2 – 4b2 + 28bc – 49c2
= 25a2 – [4b2 – 28bc + 49c2]
{ ∵ a2 – 2ab + b2 = (a – b)2}
= (5a)2 – [(2b)2 – 2 x 2b x 7c + (7c)2]
= (5a)2 – (2b – 7c)2
{ ∵ (a2 – b2 = (a + b)(a – b)}
= (5a + 2b – 7c) (5a – 2b + 7c)

Question 25.
Solution:
9a2 – b2 + 4b – 4
= 9a2 – (b2 – 4b + 4)
= (3a)2 – [(b)2 – 2 x b x 2 + (2)2]
= (3a)2 – (b – 2)2
{ ∵ a2 – 2ab + b2 = (a – b)2}
= (3a + b – 2)(3a – b + 2)
{ ∵ a2 – b2 = (a + b)(a – b)}

Question 26.
Solution:
(10)2 – (x – 5)2
= (10)2 – (x – 5)2
= (10 + x – 5)(10 – x + 5)
= (5 + x) (15 – x) Ans.

Question 27.
Solution:
{(405)2 – (395)2}
= (405)2 – (395)2
= (405 + 395) (405 – 395)
{ ∵ a2 – b2(a + b) (a – b)}
= 800 x 10 = 8000

Question 28.
Solution:
(7.8)2 – (2.2)2
= (7.8 + 2.2) (7.8 – 2.2)
= 10.0 x 5.6
= 56 Ans.

Hope given RS Aggarwal Solutions Class 8 Chapter 7 Factorisation Ex 7B are helpful to complete your math homework.

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