Question

Evaluate the following products without multiplying directly:

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

Answer 1

(i) 103 × 107

= (100 + 3) (100 + 7)

= (100)2 + (3 + 7) 100 + (3) (7)

[By using the identity (x + a)(x + b) = x2 + (a + b)x + ab,

where x = 100, a = 3, and b = 7]

= 10000 + 1000 + 21

= 11021

(ii) 95 × 96

= (100 − 5) (100 − 4) = (100)2 + (− 5 − 4) 100 + (− 5) (− 4)

[By using the identity(x + a)(x + b) = x2 + (a + b)x + ab ,

where x = 100, a = −5, and b = −4]

= 10000 − 900 + 20

= 9120

(iii) 104 × 96

= (100 + 4) (100 − 4)

= (100)2 − (4)2 [(x + y)(x - y)

= x2 - y2]

= 10000 − 16

= 9984