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Question

Evaluate 102×98 using suitable standard identity.

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Solution

Using the identity (x+a)(x+b) = x2+(a+b)x+ab
Writing 102 as 100+2 and 98 as 1002
Hence (100+2)(1002) = 1002+[2+(2)]100+(2)(2)
= 10000+(0)1004
= 9996
The answer is 9996

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