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Question
Using binomial theorem, write down the expansions :
(iv) \[\left( 1 - 3x \right)^7\]
Solution
(iv) (1 − 3x)7
\[=^{7}{}{C}_0 (3x )^0 -^{7}{}{C}_1 (3x )^1 + ^{7}{}{C}_2 (3x )^2 - ^{7}{}{C}_3 (3x )^3 +^{7}{}{C}_4 (3x )^4 - ^{7}{}{C}_5 (3x )^5 +^{7}{}{C}_6 (3x )^6 -^{7}{}{C}_7 (3x )^7 \]
\[ = 1 - 7 \times 3x + 21 \times 9 x^2 - 35 \times 27 x^3 + 35 \times 81 x^4 - 21 \times 243 x^5 + 7 \times 729 x^6 - 2187 x^7 \]
\[ = 1 - 21x + 189 x^2 - 945 x^3 + 2835 x^4 - 5103 x^5 + 5103 x^6 - 2187 x^7\]
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