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Question

Using Binomial theorem, evaluate (99)5

Solution
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(99)5=(1001)5
=5C0(100)55C1(100)4(1)+5C2(100)3(1)25C3(100)2(1)3+5C4(100)(1)45C5(1)5
=(100)55(100)4+10(100)310(100)2+5(100)1
=10000000000500000000+10000000100000+5001
=10010000500500100001
=9509900499

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