Using binomial theorem, find the value of $(103)^{4}$

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Solution

By the binomial expansion, we have
$(103)^{4} = (100 + 3)^{4} =^{4} C_{0} . (100)^{4} +^{4} C_{1} \times (100)^{3} \times 3 +^{4} C_{2} \times (100)^{2} \times 3^{2} +^{4} C_{3} \times 100 \times 3^{3} +^{4} C_{4} \times 3^{4} = (100)^{4} + 12 \times (100)^{3} + 54 \times (100)^{2} + 108 \times 10081 = 100000000 + 12 \times 1000000 + 540000 + 10800 + 81 = 100000000 + 12000000 + 540000 + 10800 + 81 = 112550881 H e n c e, (103)^{4} = 112550881$

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