Evaluate these using identity:

(i) 55 × 45 (ii) 33 × 27

(iii) 8.5 × 9.5 (iv) 102 × 98

(i) 55 × 45

We can split 55 as (50+5)

And 45 as (50–5)

Now 55 × 45

= (50+5) (50–5)

Using the identity (a +b) (a–b) = a² – b²

Here a = 50 and b = 5

= 50² – 5²

= 2500 –25

= 2475

(ii) 33 × 27

= (30+3) (30–3)

Using the identity (a +b) (a–b) = a² – b²

Here a = 30 and b = 3

= (30)² – 3²

= 900 – 9

= 891

(iii) 8.5 × 9.5

= (9 – 0.5) (9 + 0.5)

Using the identity (a +b) (a–b) = a² – b²

Here a = 9 and b = 0.5

= 9² – (0.5)²

= 81 – 0.25

= 80.75

(iv) 102 × 98

= (100 + 2) (100 – 2)

Using the identity (a +b) (a–b) = a² – b²

Here a = 100 and b = 2

= (100)² – 2²

= 10000 – 4

= 9996