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Question

Using binomial theorem, find the value of (99)4.

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Solution

By the binomial expansion, we have

(99)4=(1001)4=4C0×(100)44C1×(100)3×1+4C2×(100)2×124C3×100×13+4C4×14=(100)44×(100)3+6×(100)24×100+1=1000000004000000+60000400+1=96059601Hence,(99)4=96059601


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