# Evaluate the following products without multiplying directly:

(i) 103 × 107 (ii) 95 × 96 (iii) 104 × 96

**Solution:**

Using algebraic Identities,

(x + a)(x + b) = x^{2} + (a + b)x + ab

(a + b)(a - b) = a^{2} - b^{2}

**(i)** 103 × 107

Identity: (x + a) (x + b) = x^{2} + (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) = x^{2} + (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) = a^{2} - b^{2}

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

**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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