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Find ((x^(2)-y^(2))^(3) + (y^(2) -z^(2)...

Find `((x^(2)-y^(2))^(3) + (y^(2) -z^(2))^(3)+ (z^(2) -x^(2))^(3))/((x-y)^(3) + (y-z)^(3) + (z-x)^(3))`

A

`3(x+y) (y+z) (z+x)`

B

`3(x+y) (y+z) (z-x)`

C

`(x+y) (y+z) (z+x)`

D

`9(x+y) (y+z) (z+x)`

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The value of the expression ((x ^(2) - y ^(2)) ^(3) + ( y ^(2) - z ^(2)) ^(3) + (z ^(2) - x ^(2)) ^(3))/((x - y) ^(3) + ( y - z) ^(3) + (z - x ) ^(3)) is

Factorize: (3x-2y)^(3)+(2y-4z)^(3)+(4z-3x)^(3)

Factorize : (x-2y)^(3)+(2y-3z)^(3)+(3z-x)^(3)

If x + y + z = xyz , prove that (3x -x^(3))/ (1-3x^(2)) + (3y -y^(3))/(1- 3y^(2)) +(3z -z^(3))/(1- 3z^(2)) = (3x -x^(3))/(1-3x)^(2) * (3y- y^(3))/(1-3x)^(2)* (3z- z^(3))/(1-3z)^(2) .

verify that: x^(3)+y^(3)+z^(3)-3xyz=((1)/(2))(x+y+z)((x-y)^(2)+(y-z)^(2)+(z-x)^(2))

Prove that x^(3)+y^(3)+z^(3)-3xyz=(1)/(2)(x+y+z)[(x-y)^(2)+(y-z)^(2)+(z-x)^(2)]

Verify that x^(3)+y^(3)+z^(3)-3xyz=(1)/(2)(x+y+z)[(x-y)^(2)+(y-z)^(2)+(z-x)^(2)]

Verify that x^(3)+y^(3)+z^(3)-3xyz=(1)/(2)(x+y+z)[(x-y)^(2)+(y-z)^(2)+(z-x)^(2)]

ADVANCED MATHS BY ABHINAY MATHS ENGLISH-ALGEBRA THEORY-Example
  1. If a+b+c= 0 find a^(3) + b^(3) + c^(3) + 3abc

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  2. Find (a-b)^(3) + (b-c)^(3) + (c-a)^(3)= ?

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  3. Find ((x^(2)-y^(2))^(3) + (y^(2) -z^(2))^(3)+ (z^(2) -x^(2))^(3))/((x...

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  4. What will be factors of (a^(2)-b^(2))^(3) + (b^(2) -c^(2))^(3) + (c^(2...

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  5. If x+ y+ z= 2s find (s-x)^(3) + (s-y)^(3) + 3(s-x) (s-y) z= ?

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  6. If a= 1.21, b= 2.23 & c= -3.44 find a^(3) + b^(3) +c^(3) + 3abc= ?

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  7. If a= 5.431, b= 2.121 & c= -7.552 find a^(3) +b^(3) + c^(3) + 3abc= ?

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  8. If a^((1)/(3)) + b^((1)/(3)) = c^((1)/(3)) then which option is correc...

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  9. If a^(2) + b^(2) = c^(2) then find (a^(6) + b^(6)- c^(6))/(a^(2) b^(2)...

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  10. If (1)/(a+1) + (1)/(1+b) + (1)/(1 + c) =1 find (a)/(1+a) + (b)/(1+b)...

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  11. If (1)/(x+1) + (2)/(y+2) + (1009)/(z+ 1009)=1 find (x)/(x+1) + (y)/(y+...

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  12. If (a)/(x-a) + (b)/(y-b) + (c )/(z-c)=2 find (x)/(x-a) + (y)/(y-b) + ...

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  13. If (a)/(x-1) + (4b)/(y-2b) + (9c)/(z-3c)= 6-a find (ax)/(x-1) + (2y)/(...

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  14. If (a)/(b+c) + (b)/(c+a) + (c )/(a+b)= 1 find (a^(2))/(b+c) + (b^(2))/...

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  15. If (a^(2)-bc)/(a^(2) +bc) + (b^(2)-ac)/(b^(2) + ac) + (c^(2)-ab)/(c^(2...

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  16. Given, a^(2) =b+c, b^(2)=c + a " & " c^(2) = a + b or (a^(2))/(b+c) = ...

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  17. Given, a^(2) =b+c, b^(2)=c + a " & " c^(2) = a + b or (a^(2))/(b+c) = ...

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  18. (x^(2))/(by + cz) = (y^(2))/(ax + cz)= (z^(2))/(ax + by)=1 find (a)/...

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  19. (x^(2))/(by + cz) = (y^(2))/(ax + cz)= (z^(2))/(ax + by)=1 find (x)...

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  20. If (x^(2))/(by+cz) = (y^(2))/(ax+ cz) = (z^(2))/(ax + by)=2 (a)/(x+...

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