Question

Evaluate the following products without mulitplying directly :

(i) 103 × 107

(ii) 95 × 96

(iii) 104 × 96

Answer 1

(i) 103 × 107

= (100 + 3) (100 – 3)

As per Identity, (a + b)(a – b)

= a2 – b2 (100 + 3)(100 – 3)

= (100)2 – (3)2 = 10000 – 9

= 9991

(ii) 95 × 96 = (100 – 5) (100 + 6)

As per Identity. (x + a) (x + b)

= x2 + (a + b)x + ab (100 – 5) (100 + 6)

= (100)2+(-5 + 6)100 + (-5 × 6)

= 10000 + (1)100 + (-30)

= 10000 + 100 – 30

= 10100 – 30 = 10070

(iii) 104 × 96 = (100 + 4) (100 – 4)

As per Identity, (a + b) (a – b)

= a2 – b2 (100 + 4) (100 – 4)

= (100)2 – (4)2 = 10000 – 16

= 9984