# Evaluate these us

(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

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