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Question
Evaluate of the following:
1113 − 893
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Solution
In the given problem, we have to find the value of numbers
Given 1113 − 893
We can write 1113 − 893 as `(100+ 11)^3 - (100 - 11)^3`
We shall use the identity `(a+b)^3 - (a-b)^3 = 2[b^3 + 3a^2b]`
Here a=100 , b = 11
\[{111}^3 - {89}^3 = \left( 100 + 11 \right)^3 - \left( 100 - 11 \right)^3\]
`= 2[11^3 + 3 (100)^2(11)]`
`= 2 [1331 + 330000]`
`= 2 [331331]`
` = 662662`
Hence the value of 1113 − 893 is 662662 .
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