Using suitable identity, evaluate the following:
ti)998^2
(ii) (102)^2-(98)^2
(iv) 306×294
(viii) (9.7)^2 – (0.3)^2
(vii) 112.6 87.4
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Step-by-step explanation:
i. (1000 - 2)^2
1000^2 + 2^2 - 2 x 1000 x 2
1000000 + 4 - 4000
996004
Using (a-b)^2 = a^2 + b^2 - 2ab
ii. (100+2)^2 - (100-2)^2
100^2 + 2^2 + 2 x 100 x 2 - [ 100^2 + 2^2 - 2x100x2]
10000 + 4 + 400 - 10000 - 4 + 400
400 + 400
800
Using (a+b)^2 = a^2 + b^2 + 2ab
and (a-b)^2 = a^2 + b^2 - 2ab
iv. (300 + 6) x (300 - 6)
300^2 - 6^2
90000 - 36
89964
Using (a+b)(a-b) = a^2 - b^2
viii. (9.7)^2 - (0.3)^2
(9.7 + 0.3) x (9.7 - 0.3)
10.0 x 9.4
94
Using a^2 - b^2 = (a+b)(a-b)
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