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Expand using binomial theorem: (i) (1...

Expand using binomial theorem:
`(i) (1-2x)^(4) " " (ii) (x+2y)^(5)`
`(iii) (x-(1)/(x))^(6) " "(iv) ((2x)/(3)=(3)/(2x))^(5)`
`(v) (x^(2) +(2)/(x))^(6)" "(vi) (1+(1)/(x^(2)))^(4)`

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Verified by Experts

The correct Answer is:
`(i) 1-8x+24x^(2)-32x^(3)+16x^(4)`
`(ii) x^(5)+10x^(4)y+40x^(3)y^(2)+80x^(2)y^(3)+80xy^(4)+32y^(5)`
`(iii) x^(6)=6x^(4)+15x^(2)-20+(15)/(x^(2))-(6)/(x^(4))+(1)/(x^(6))`
`(iv)(32x^(5))/(243)=(40x^(3))/(27)+(20x)/(3)-(15)/(x)+(135)/(8x^(3))-(243)/(32x^(5))`
`(v) x^(12)+12x^(9)+60x^(6)+160x^(3)+240+(192)/(x^(3))+(64)/(x^(6))`
`(vi) 1+(4)/(x^(2))+(6)/(x^(4))+(4)/(x^(6))+(1)/(x^(8))`
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NAGEEN PRAKASHAN-BINOMIAL THEOREM-Example
  1. Expand using binomial theorem: (i) (1-2x)^(4) " " (ii) (x+2...

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  2. Using binomial theorem, write down the expansions of the following: (2...

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  3. Expand (3x-2y)^(6) with the help ob binomial theorm.

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  4. Simplify with the help of binomial theorm.

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  5. (iii) Find an approximate value of (0.99)^5 using the first three term...

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  6. Using binomial theorem, prove that (101)^(50)> 100^(50)+99^(50)dot

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  7. If number of terms in the expansion of (x -2y +3z)^n are 45, then n i...

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  8. Prove that overset(n)underset(r=0)(Sigma^(n))C(r).4^(r)=5^(n)

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  9. If (1-x+x^(2))^(4)=1+P(1)x+P(2)x^(2)+P(3)x^(3)+...+P(8)x^(8), then pro...

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  10. If o be the sum of odd terms and E that of even terms in the expansion...

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  11. Find the 8th term in the expansion of ((2x)/(3)-(3)/(5x))^(12)

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  12. Find the 13^(t h)term in the expansion of (9x-1/(3sqrt(x)))^(18),x!=0

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  13. Find the 15th term in the expansion of "("sqrt(x)-sqrt(y)")"^(17)

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  14. Find the middle term in the expansion of (3x-(1)/(2x))^(16)

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  15. Find the middle term in the expansion of (1+2x+x^(2))^(10)

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  16. Find the 4th term from the end in the expansion of (1-3x)^(10)

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  17. Show that the middle term in the expansion of (1+x)^(2n)i s((1. 3. 5 (...

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  18. how that the coefficient of (r+1) th in the expansion of (1+x)^(n+1) ...

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  19. If in any binomial expansion a, b, c and d be the 6th, 7th, 8th and 9t...

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  20. Find the coefficient of x^(6) in the expansion of (2x^(3)-(1)/(3x^(3))...

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  21. Find the coefficient of x^(7) in the expansion of (2x^(2)-(1)/(x))^(2...

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