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Mathematics

Using (a - b)2 = (a2 + b2 - 2ab), evaluate:

(i) (97)2

(ii) (992)2

(iii) (9.98)2

Expansions

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Answer

(i) Given,

⇒ (97)2

⇒ (100 - 3)2

Using identity :

⇒ (a - b)2 = a2 + b2 - 2ab

⇒ (100 - 3)2 = (100)2 + 32 - 2 × 100 × 3

⇒ (100 - 3)2 = 10000 + 9 - 600

⇒ 9409.

Hence, (97)2 = 9409.

(ii) Given,

⇒ (992)2

⇒ (1000 - 8)2

Using identity :

(a - b)2 = a2 + b2 - 2ab

⇒ (1000 - 8)2 = (1000)2 + 82 - 2 × 1000 × 8

⇒ (1000 - 8)2 = 1000000 + 64 - 16000

⇒ 984064.

Hence, (992)2 = 984064.

(iii) Given,

⇒ (9.98)2

⇒ (10 - 0.02)2

Using identity :

(a - b)2 = a2 + b2 - 2ab

⇒ (10 - 0.02)2 = (10)2 + 0.022 - 2 × 10 × 0.02

⇒ (10 - 0.02)2 = 100 + 0.0004 - 0.4

⇒ 99.6004

Hence, (9.98)2 = 99.6004.

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