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The total number of different terms in t...

The total number of different terms in the product `(.^(101)C_(0) - .^(101)C_(1)x+.^(101)C_(2)x^(2)-"….."-.^(101)C_(101)x^(101))(1+x+x^(2)+"…."+x^(100))^(101)` is `"____"`.

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The correct Answer is:
102
`(.^(101)C_(0).^(101)C_(1)x+.^(101)C_(2)x^(2)-"...."-.^(101)C_(101)x^(101))(1+x+x^(2)+"...." +x^(100))^(101)`
`= (1-x)^(101).((1-x^(101))/(1-x))^(101)`
`= (1-x^(101))^(101)`
`:.` Number of different terms `= 102`
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