Question

Can’t you easily find the products below like this?

(i) 51 × 49

(ii) 98 × 102

(iii) 10.2 × 9.8

(iv) 7.3 × 6.7

Answer 1

We know that (x − y)(x + y) = x² − y²

(i)

The number 51 can be written as (50 + 1) and 49 can be written as (50 − 1).

∴ 51 × 49 = (50 + 1) (50 − 1)

= 50² − 1²

= 2500 − 1

= 2499

(ii)

The number 98 can be written as (100 − 2) and 102 can be written as (100 + 2).

∴ 98 × 102 = (100 − 2) (100 + 2)

= (100)² − 2²

= 10000 − 4

= 9996

(iii)

The number 10.2 can be written as (10 + 0.2) and 9.8 can be written as (10 − 0.2).

∴ 10.2 × 9.8 = (10 + 0.2) (10 − 0.2)

= (10)² − (0.2)²

= 100 − 0.04

= 99.96

(iv)

The number 7.3 can be written as (7 + 0.3) and 6.7 can be written as (7 − 0.3).

7.3 × 6.7 = (7 + 0.3) × (7 − 0.3)

= 7² − (0.3)²

= 49 − 0.09

= 48.91