Evaluate the following products without multiplying directly:
(i) 103 × 107    (ii) 95 × 96    (iii) 104 × 96

Solution:

Using algebraic Identities,

(x + a)(x + b) = x² + (a + b)x + ab

(a + b)(a - b) = a² - b²

(i) 103 × 107

Identity: (x + a) (x + b) = x² + (a + b)x + ab

103 × 107 = (100 + 3)(100 + 7)

Substituting x = 100, a = 3, b = 7 in the above identity, we get

= (100)² + (3 + 7)(100) + (3)(7)

= 10000 + 1000 + 21

= 11021

(ii) 95 × 96

Identity: (x + a)(x + b) = x² + (a + b)x + ab

95 × 96 = (100 - 5)(100 - 4)

Substituting x = 100, a = -5, b = -4 in the above identity, we get

= (100)² + (-5 - 4)(100) + (-5)(-4)

= 10000 - 900 + 20

= 9120

(iii) 104 × 96

Identity: (a + b)(a - b) = a² - b²

104 × 96 = (100 + 4)(100 - 4)

Substituting a = 100, b = 4 in the above identity, we get

= (100)² - (4)²

= 10000 - 16

= 9984

☛ Check: NCERT Solutions for Class 9 Maths Chapter 2

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Video Solution:

Evaluate the following products without multiplying directly: (i) 103 × 107    (ii) 95 × 96    (iii) 104 × 96

NCERT Solutions Class 9 Maths Chapter 2 Exercise 2.5 Question 2:

Summary:

The product of the following 103 × 107, 95 × 96, and 104 × 96 without multiplying directly are 11021, 9120, and 9984 respectively.

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