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(a) If x + y + z=0, show that x ^(3) + ...

(a) ` If x + y + z=0,` show that `x ^(3) + y ^(3) + z ^(3)= 3 xyz.`
(b) Show that ` (a-b) ^(3) + (b-c) ^(3) + (c-a)^(3) =3 (a-b) (b-c) (c-a)`

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KUMAR PRAKASHAN-POLYNOMIALS-Exercise - 2.5
  1. Evaluate the following uing suitable identities : (99)^(3)

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  2. Evaluate the following uing suitable identities : (102)^(3)

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  3. Evaluate the following uing suitable identities : (998)^(3)

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  4. Factorise each of the following (i) 8a ^(3) + b^(3) + 12a ^(2) + 6ab...

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  5. Factorise each of the following (i) 8a ^(3) + b^(3) + 12a ^(2) + 6ab...

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  6. Factorise each of the following : 27-125a^(3)-135a + 225a^(2)

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  7. Factorise each of the following : 64a^(3) - 27b^(3) - 144a^(2)b + 10...

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  8. Factorise each of the following : 27p^(3) - (1)/(216)-(9)/(2)p^(2) +...

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  9. Verify (i) x ^(3) + y ^(3) = (x + y) (x ^(2) -xy + y ^(2)) (ii) ...

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  10. Verify (i) x ^(3) + y ^(3) = (x + y) (x ^(2) -xy + y ^(2)) (ii) ...

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  11. Factorise each of the following : 27y^(3) + 125z^(3)

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  12. Factorise each of the following : 64m^(3) - 343 n^(3)

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  13. Factorise 27 x ^(3) + y ^(3) + z ^(3)-9 xyz using identitiy.

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

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  15. (a) If x + y + z=0, show that x ^(3) + y ^(3) + z ^(3)= 3 xyz. (b) ...

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

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

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  18. Gi ven possible expressions for the length and breadth of the rectangl...

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

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  20. What are the possible polynomial expressions for the dimensions of the...

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