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