1.

Evaluate each of the following using identities:(i) (399)2(ii) (0.98)2(iii) 991×1009(iv) 117×83

Answer»

(i) We will use the identity, (a - b)2 = a2 + b2 – 2ab

(399)2 = (400 - 1)2

= (400)2 + (1)2 - 2 x 400.1

= 16000 + 1 - 800

= 159201

(ii) We will use the identity, (a - b)2 = a2 + b2 – 2ab

(0.98)2 = (1 - 0.02)2

 = (1)2 + (0.02)2 - 2 x 0.02 x 1

= 1 + 0.004 - 0.04

= 0.9604

(iii) We will use the identity, (a - b)(a + b)= a2 - b2

991 x 1009 = (1000 - 9)(1000 + 9)

= (1000)2 - (9)2

= 1000000 - 81

= 999919

(iv) We will use the identity, (a - b) (a + b)= a2 - b2

117 x 83 = (100 + 17)(100 - 17)

= (100)2 + (17)2

= 10000 - 289

= 9711



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