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Using binomial theorem, expand {(x+y)^5+...

Using binomial theorem, expand `{(x+y)^5+(x-y)^5}dot` and hence find the value of `{(sqrt(2)+1)^5+(sqrt(2)-1)^5}dot`

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The correct Answer is:
`(i) 2(a^(5)+10a^(3)b^(2)+5ab^(4)),58sqrt(2)" "(ii) 2(32x^(6)-48x^(4)+18x^(2)-1)`
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NAGEEN PRAKASHAN-BINOMIAL THEOREM-Example
  1. Using binomial theorem, expand {(x+y)^5+(x-y)^5}dot and hence find the...

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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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