RS Aggarwal Class 8 Math Seventh Chapter Factorisation Exercise 7B Solution
EXERCISE 7B
Factorise:
FORMULA: (a2 – b2) = (a + b) (a – b)
(1) x2 – 36
= x2 – 62
= (x – 6) (x + 6)
(2) 4a2 – 9
= (2a)2 – (3)2
= (2a – 3) (2a + 3)
(3) 81 – 49x2
= (9)2 – (7x)2
= (9 – 7x) (9 + 7x)
(4) 4x2 – 9y2
= (2x)2 – (3y)2
= (2x – 3y) (2x + 3y)
(5) 16a2 – 225b2
= (4a)2 – (15b)2
= (4a – 15b) (4a + 15b)
(6) 9a2b2 – 25
= (3ab)2 – (5)2
= (3ab – 5) (3ab + 5)
(7) 16a2 – 144
= (4a)2 – (12)2
= (4a – 12) (4a + 12)
= [4(a – 3)] [4(a + 3)]
= (4 × 4) (a – 3) (a + 3)
= 16 (a – 3) (a + 3)
(8) 63a2 – 112b2
= 7(9a2 – 16b2)
= 7 [(3a)2 – (4b)2]
= 7 (3a – 4b) (3a + 4b)
(9) 20a2 – 45b2
= 5(4a2 – 9b2)
= 5 [(2a)2 – (3b)2]
= 5 (2a – 3b) (2a + 3b)
(10) 12x2 – 27
= 3(4x2 – 9)
= 3[(2x)2 – (3)2]
= 3 (2x – 3) (2x + 3)
(11) x3 – 64x
= x[(x)2 – (8)2]
= x (x – 8) (x + 8)
(12) 16x5 – 144x3
= 16x3 (x2 – 9)
= 16x3 [(x)2 – (3)2]
= 16x3 (x – 3) (x + 3)
(13) 3x5 – 48x3
= 3x3[(x)2 – 16]
= 3x3[(x)2 – (4)2]
= 3x3 (x – 4) (x + 4)
(14) 16p3 – 4p
= 4p (4p2 – 1)
= 4p [(2p)2 – (1)2]
= 4p (2p – 1) (2p + 1)
(15) 63a2b2 – 7
= 7 (9a2b2 – 1)
= 7 [(3ab)2 – (1)2]
= 7 (3ab – 1) (3ab + 1)
(16) 1 – (b – c)2
= (1)2 – (b – c)2
= (1 – b + c) (1 + b – c)
(17) (2a + 3b)2 – 16c2
= (2a + 3b)2 – (4c)2
= (2a + 3b – 4c) (2a + 3b + 4c)
(18) (l + m)2 – (l – m)2
= (l + m + l – m) (l + m – l + m)
= 2l × 2m = 4lm
(19) (2x + 5y)2 – 1
= (2x + 5y)2 – (1)2
= (2x + 5y – 1) (2x + 5y + 1)
(20) 36c2 – (5a + b)2
= (6c)2 – (5a + b)2
= (6c + 5a + b) (6c – 5a – b)
(21) (3x – 4y)2 – 25z2
= (3x – 4y)2 – (5z)2
= (3x – 4y + 5z) (3x – 4y – 5z)
(22) x2 – y2 – 2y – 1
= x2 – (y2 + 2y + 1)
= x2 – (y + 1)2
= (x + y + 1) (x – y – 1)
(23) 25 – a2 – b2 – 2ab
= 25 – (a2 + 2ab + b2)
= (5)2 – (a + b)2
= (5 + a + b) (5 – a – b)
(24) 25a2 – 4b2 + 28bc – 49c2
= 25a2 – [(2b)2 – (2 × 2b × 7c) + (7c)2]
= (5a)2 – (2b – 7c)2
= (5a + 2b – 7c) (5a – 2b + 7c)
(25) 9a2 – b2 + 4b – 4
= 9a2 – [(b)2 – (2 × b × 2) + (2)2]
= (3a)2 – (b – 2)2
= (3a + b – 2) (3a – b + 2)
(26) 100 – (x – 5)2
= (10)2 – (x – 5)2
= (10 + x – 5) (10 – x + 5)
= (5 + x) (15 – x)
(27) Evaluate {(405)2 – (395)2}
= (405 + 395) (405 – 395)
= 800 × 10 = 8000
(28) Evaluate {(7.8)2 – (2.2)2}
= (7.8 + 2.2) (7.8 – 2.2)
= 10 × 5.6 = 56
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