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

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

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The correct Answer is:
`(z-x) ^(2)`
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SWAN PUBLICATION-POLYNOMIALS -EXERCISE 2.5
  1. Evaluate the following using suitable identity : (102)^3.

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  2. Evaluate the following using suitable identity : (998)^3.

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  3. Factorise the following : 8a^3+b^3+12a^2b+6ab^2.

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  4. Factorise each of the following: 8a^3- b^3-12a^2b + 6ab^2

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  5. Factorise the following : 27-125a^3-135a+225a^2.

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  6. Factorise ech of the 64 a ^(3) - 27 b ^(3) - 144 a ^(2) b + 108 ab ^...

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  7. Factorise the following : 27p^3-1/216-9/2p^2+1/4p.

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  8. Simplify (x + y) (x ^(2) + xy + y ^(2))

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  9. Prove that x ^(3) - y ^(3) = (x - y) (x ^(2) + xy + y ^(2))

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  10. Factorise each of the following: 27y^(3) + 125x^(3)

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  11. Factorise the following : 64m^3 - 343n^3.

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  12. Factorise : 27x^3+y^3+z^3-9xyz.

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

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  14. If x + y + z = 0, show that x^3 + y^3 + z^3 = 3xyz.

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  15. Without actually calculating the cubes, find the value of each of the ...

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  16. Without actually calculating the cubes, find the value of each of the ...

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  17. Give possible expressions for the length and breadth of each of the fo...

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  18. Give possible expressions for the length and breadth of each of the fo...

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  19. What are the possible expressions for the dimensions of the cuboids wh...

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  20. What are the possible expressions for the dimensions of the cuboids wh...

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