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Question
Using binomial theorem evaluate .
(iv) (98)5
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Solution
\[(100 - 2 )^5 \]
\[ =^{5}{}{C}_0 \times {100}^5 \times 2^0 + -^5 C_1 \times {100}^4 \times 2^1 + ^{5}{}{C}_2 \times {100}^3 \times 2^2 - ^{5}{}{C}_3 \times {100}^2 \times 2^3 + ^{5}{}{C}_4 \times {100}^1 \times 2^4 -^{5}{}{C}_5 \times {100}^0 \times 2^5 \]
\[ = 10000000000 - 1000000000 + 40000000 - 800000 + 8000 - 32\]
\[ = 9039207968\]
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