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Using binomial theorem, evaluate : (101)...

Using binomial theorem, evaluate : `(101)^4`

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The correct Answer is:
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`(101)^(4)=(100+1)^(4)`
`=^(5)C_(0)(100)^(4)(1)^(0)+^(4)C_(1)(100)^(3)(1)^(1)`
`+^(4)C_(2)(100)^(2)(1)^(2)+^(4)C_(3)(100)^(1)(1)^(3)`
`+^(4)C_(4)(100)^(0)(1)^(4)`
`=^(4)C_(0)(100)^(4)+^(4)C_(1)(100)^(3).1+^(4)C_(2)(100)^(2).1`
`+^(4)C_(3)(100).1+^(4)C_(4)1.1`
`=(1xx100000000)+(4xx1000000xx1)`
`+ (6xx 10000xx1)+(4xx100xx1)`
`+(6xx10000xx1)+(4xx100xx1)+(1xx1xx1)`
`=100000000+4000000+60000+400+1`
`=104060401`
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