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Question
Evaluate following using identities:
991 ☓ 1009
Solution
In the given problem, we have to evaluate expressions by using identities.
The given expression is 991 x 1009
We have `(991 + 1009)/2 = 1000`
So we can express 991 and 1009 in the terms of 1000 as
991 = 1000 - 9
1009 = 1000 + 9
`991 xx 1009 = (1000 - 9)(1000 + 9)`
We shall use the identity `(x - y)(x + y) = x^2 - y^2`
Here
(x - y) = (1000 - 9)
(x + y) = (1000 + 9)
By applying in identity we get
`(1000 - 9)(1000 + 9) = (1000)^2 - (9)^2`
= 1000000 - 81
= 999919
Hence the value of 991 x 1009 is 999919
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