Using binomial theorem, find the value of $(99)^{4}$ .

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Solution

By the binomial expansion, we have

$(99)^{4} = (100 - 1)^{4} =^{4} C_{0} \times (100)^{4} -^{4} C_{1} \times (100)^{3} \times 1 +^{4} C_{2} \times (100)^{2} \times 1^{2} -^{4} C_{3} \times 100 \times 1^{3} +^{4} C_{4} \times 1^{4} = (100)^{4} - 4 \times (100)^{3} + 6 \times (100)^{2} - 4 \times 100 + 1 = 100000000 - 4000000 + 60000 - 400 + 1 = 96059601 Hence, (99)^{4} = 96059601$

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