Answer :

(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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