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प्रश्न
Using binomial theorem, write down the expansions :
(v) \[\left( ax - \frac{b}{x} \right)^6\]
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उत्तर
(v) \[(ax - \frac{b}{x} )^6 \]
\[ =^{6}{}{C}_0 (ax )^6 (\frac{b}{x} )^0 - ^{6}{}{C}_1 (ax )^5 (\frac{b}{x} )^1 + ^{6}{}{C}_2 (ax )^4 (\frac{b}{x} )^2 - ^{6}{}{C}_3 (ax )^3 (\frac{b}{x} )^3 +^{6}{}{C}_4 (ax )^2 (\frac{b}{x} )^4 - ^{6}{}{C}_5 (ax )^1 (\frac{b}{x} )^5 + ^{6}{}{C}_6 (ax )^0 (\frac{b}{x} )^6\]
\[ = a^6 x^6 - 6 a^5 x^4 b + 15 a^4 x^2 b^2 - 20 a^3 b^3 + 15\frac{a^2 b^4}{x^2} - 6\frac{a b^5}{x^4} + \frac{b^6}{x^6}\]
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\[= ^{5}{}{C}_0 (2x )^5 (3y )^0 +^{5}{}{C}_1 (2x )^4 (3y )^1 + ^{5}{}{C}_2 (2x )^3 (3y )^2 + ^{5}{}{C}_3 (2x )^2 (3y )^3 + ^{5}{}{C}_4 (2x )^1 (3y )^4 +^{5}{}{C}_5 (2x )^0 (3y )^5\]
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