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Verify that x ^(3) + y ^(3) + z ^(3) - ...

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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{:[( x,x^(2) , 1+ px^(3) ),( y,y^(2) , 1+ py^(3)),( z,z^(2) , 1+pz^(3)) ]:} =( 1+pxyz ) ( x-y) ( y-z ) (z-x) , where p is any scalar .

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NCERT TAMIL-POLYNOMIALS AND FACTORISATION -EXERCISE 2.5
  1. Use suitable idntities to find the following products (i) (x +5) (x ...

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  2. Evaluate the following products without actual multiplication. (i) 1...

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  3. Factorise the following using appropriate identities. (i) 16x ^(2) +...

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  4. Expand each of the following, using suitable identities (i) (x + 2y+...

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  5. Factories (i) 25 x ^(2) + 16 y ^(2) + 4z ^(2) - 40 xy + 16 yz - 20zx...

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  6. If a + b +c =9 and ab + bc + ca =26, then find a ^(2) + b ^(2) + c ^(2...

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  7. Evaluate the following using suitable identites. (i) (99) ^(3) " "(...

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

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

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  10. Faactorise (i) 27a ^(3) + 64 b ^(3) (ii) 343 y ^(3) -1000 using th...

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

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

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

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  14. Without actual calculating the cubes, find the vlaue of each of the fo...

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

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

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  17. If 2 (a ^(2) + b ^(2)) = (a+b)^(2), then show that a =b

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