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

Expand using binomial theorem:
`(i) (1-2x)^(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 ENGLISH-BINOMIAL THEOREM-Exercise 8A
  1. Find the value of (sqrt(2)+1)^6-(sqrt(2)-1)^6dot

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  2. If x= sqrt5+sqrt3 and y = sqrt5-sqrt3, then x^4 -y^4

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  3. Find the values of the following using binomial theorem: (i) 49^(4)...

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  4. By using binomial theorem find which number is greater (1.2)^(3000) " ...

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  5. Prove that Sigma(r=0)^(n) ""^(n)C(r).3^(r)=4^(n)

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  6. If n is a positive integer then find the number of terms in the expans...

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  7. Find the number of terms in the expansion of (1+3x+3x^(2)+x^(3))^(15)

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  8. If (1+x+x^(2))^(n)=1 +a(1)x+a(2)x^(2)+a(3)x^(3) +……..+a(2n).x^(2...

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  9. Using binomial theorem, prove that 2^(3n)-7n-1 is divisible by 49 , wh...

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  10. Expand using binomial theorem: (i) (1-2x)^(4)

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  11. Evaluate using binomial theorem: (i) (sqrt(2)+1)^(6) +(sqrt(2)-1)^(6...

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  12. Using binomial theorem, expand {(x+y)^5+(x-y)^5}dot and hence find the...

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  13. Expand (x+y)^(4)-(x-y)^(4). Hence find the value of (3+sqrt(5))^(4) -(...

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  14. Find the values of the following using binomial theorem: (i) 49^(4)...

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  15. By using binomial theorem find which number is greater (1.2)^(3000) " ...

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  16. Prove that Sigma(r=1) ""^(n)C(r).3^(r)=4^(n)

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  17. If n is a positive integer then find the number of terms in the expans...

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  18. Find the number of terms in the expansion of (1+3x+3x^(2)+x^(3))^(15)

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  19. If (1-x+x^2)^n=a0+a1x+a2x^2+ .........+a(2n)x^(2n),\ find the value o...

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  20. By using binomial theorem prove that (2^(3n)-7n-1) is divisible by ...

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