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Using binomial theorem, write down the e...

Using binomial theorem, write down the expansions of the following: `(root(3)(x)-root(3)(a))^6`

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`=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}-20 x a+15 x^{2 / 3} a^{4 / 3}-6 x^{1 / 3} a^{5 / 3}+a^{2}`
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RD SHARMA-BINOMIAL THEOREM-Solved Examples And Exercises
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  2. Using binomial theorem, write down the expansions of the following: (1...

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  3. Using binomial theorem, write down the expansions of the following: ...

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  8. Using binomial theorem, write down the expansions of the following: \ ...

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  9. Using binomial theorem, write down the expansions of the following: \ ...

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  10. Using binomial theorem, write down the expansions of the following:\ (...

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  11. Evaluate the following: (sqrt(x+1)+sqrt(x-1))^6+(sqrt(x+1)-sqrt(x-1))^...

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  12. Evaluate the following: \ (3+sqrt(2))^5-(3-sqrt(2))^5

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  13. Evaluate the following: \ (1+2sqrt(x))^5+(1-2sqrt(x))^5

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  14. Evaluate the following: \ (sqrt(3)+1)^5-(sqrt(3)-1)^5

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  15. Evaluate the following: \ (sqrt(3)+sqrt(2))^6-(sqrt(3)-sqrt(2))^6

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  16. Evaluate the following: \ {a^2+sqrt(a^2-1)}^4+{a^2-sqrt(a^2-1)}^4

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  17. Evaluate the following: \ (x+sqrt(x^2-1))^6+(x-sqrt(x^2-1))^6

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  18. Evaluate the following: \ (sqrt(2)+1)^6+(sqrt(2)-1)^6

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  19. Evaluate the following: (2+sqrt(3))^7+(2-sqrt(3))^7

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  20. Evaluate the following: \ (0. 99)^5+(1. 01)^5

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