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If a and b are distinct integers, prove ...

If a and b are distinct integers, prove that `a- b` is a factor of `a^n -b^n`, whenever n is a positive integer. [Hint write `a^n = (a - b + b)^n` and expand]

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PSEB-BINOMIAL THEOREM-EXERCISE
  1. Write the general term in the expansion of (x^2 - y)^6

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  2. Write the general term in the expansion of (x^2 - yx)^12 , x ne 0.

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  3. Find the 4th term in the expansion of (x-2y)^12.

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  4. Find the 13th term in the expansion of (9x-1/(3sqrtx))^18, x ne 0.

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  5. Find the middle terms in the expansion of:- (3- x^3/6)^7

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  6. Find the middle terms in the expansion of:- (x/3+9y)^10.

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  7. In the expansion of (1 + a)^(m+n), prove that coefficients of a^m and ...

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  8. The coefficients of the (r-1)^(th),r^(th) and (r+1)^(th) terms in the ...

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  9. Prove that the coefficient of x^n in the expansion of (1+x)^(2n) is tw...

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  10. Find a positive value of m for which the coefficient of x^2 in the exp...

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  11. Find a, b and n in the expansion of (a+b)^n if the first three terms o...

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  12. Find a if the coefficients of x^2 and x^3 in the expansion of (3 + ax)...

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  13. Find the coefficient of x^5 in the product (1 + 2x)^6 (1 -x)^7 using b...

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

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  15. Evaluate (sqrt3+sqrt2)^6 - (sqrt3-sqrt2)^6.

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

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  17. Find an approximation of (0.99)^5 using the first three terms of its e...

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

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  19. Expand using Binomial Theorem (1+x/2-2/x)^4, x ne 0.

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

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