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Expand (3x-2y)^(4)...

Expand `(3x-2y)^(4)`

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`(3x-2y)^(6)`
`=overset(6)underset(r=0)(Sigma).^(6)C_(r)(3x)^(6-r)(-2y)^(r)`
`=^(6)C_(0)(3x)^(6)+^(6)C_(1)(3x)^(5)(-2y)^(1)+^(6)C_(2)(3x)^(4)(-2y)^(2)`
`+^(6)C_(3)(3x)^(3)(-2y)^(3)+^(6)C_(4)(3x)^(2)(-2y)^(4)`
`+^(6)C_(5)(3x)^(1)(-2y)^(5)+^(6)C_(6)(-2y)^(6)`
`=1.729x^(6)+6(243x^(5))(-2y)+15.(81x^(4))`
`(4y^(2))+20(27x^(3))(-8y)^(3)+15(9x^(2))(16y^(4))`
`+6(3x)(-32y^(5))+1.(64y^(6))`
`=729x^(6)-2916x^(5)y+4860x^(4)y^(2)-4320x^(3)y^(3)`
`=2160x^(2)y^(4)-576xy^(5)+64y^(6)`
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NAGEEN PRAKASHAN ENGLISH-BINOMIAL THEOREM-Miscellaneous Exericse
  1. Expand (3x-2y)^(4)

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  2. Find a, b and n in the expansion of (a+b)^nif the first three terms ...

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  3. If the coefficients of x^2a n d\ x^3 in the expansion o (3+a x)^9 are ...

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  4. Find the coefficient of a^4 in the product (1+a)^4(2-a)^5 using binomi...

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  5. If a and b are distinct integers, prove that a - b is a factor of a^n-...

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  6. Evaluate (sqrt(3)+sqrt(2))^6-(sqrt(3)-sqrt(2))^6dot

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  7. Find the value of (a^2+sqrt(a^2-1))^4+(a^2-sqrt(a^2-1))^4.

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  8. Find an approximation of (0. 99)^5 using the first three terms of its ...

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  9. Find n, if the ratio of the fifth term from the beginning to the fi...

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  10. Using binomial theorem expand (1+x/2-2/x)^4,\ x!=0.

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  11. Find the expansion of (3x^2-2a x+3a^2)^3 using binomial theorem.

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  12. Find a, b and n in the expansion of (a+b)^nif the first three terms ...

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  13. If the coefficients of x^2a n d\ x^3 in the expansion o (3+a x)^9 are ...

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  14. Find the coefficient of x^5 in the expansion of (1 + 2x)^6 (1-x)^7.

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  15. If a and b are distinct integers, prove that a - b is a factor of a^n-...

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  16. Evaluate (sqrt(3)+sqrt(2))^6-(sqrt(3)-sqrt(2))^6dot

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  17. Find the value of (a^2+sqrt(a^2-1))^4+(a^2-sqrt(a^2-1))^4.

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  18. Find an approximation of (0. 99)^5using the first three terms of its ...

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  19. Find n, if the ratio of the fifth term from the beginning to the fi...

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  20. Expand using Binomial Theorem (1+x/2-2/x)^4,x!=0.

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  21. Find the expansion of (3x^2-2a x+3a^2)^3 using binomial theorem.

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