Question

Simplify the following using the formula: (a – b) (a + b)= a² – b² :

(i) 197 × 203

(ii) 113 × 87

(iii) 95 × 105

Answer 1

(i) 197 × 203

We can express 203 as 200 + 3 and 197 as 200 – 3

Using formula (a – b) (a + b) = a² – b²

We get,

197 × 203 

= (200 – 3) (200 + 3)

= (200)² – (3)²

= 40000 – 9

= 39991

(ii) 113 × 87

We can express 113 as 100 + 13 and 87 as 100 – 13

Using formula (a – b) (a + b) = a² – b²

We get,

113 × 87 

= (100 – 13) (100 + 13)

= (100)² – (13)²

= 10000 – 169

= 9831

(iii) 95 × 105

We can express 95 as 100 – 5 and 105 as 100 + 5

Using formula (a – b) (a + b) = a² – b²

We get,

95 × 105 

= (100 – 5) (100 + 5)

= (100)² – (5)²

= 10000 – 25

= 9975