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

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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NAGEEN PRAKASHAN-POLYNOMIALS-Exercise 2 E
  1. Evaluate without multiplying directly : (i) 33xx27 " " (ii) 103xx9...

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  2. Expand : (i) (3a-5b)^(2) " " (ii) (a+(1)/(a))^(2) " " (iii) (2x-(...

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  3. Expand : (i) (a+b-c)^(2) " " (ii) (a-2b-5c)^(2) " " (iii) (3a-2b...

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  4. Evaluate using formula : (i) (188)^(2) " " (ii) (9.4)^(2) " " (i...

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  5. (i) If a^(2)+b^(2)+c^(2)=20 " and" a+b+c=0, " find " ab+bc+ac. (ii) ...

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  6. Expand : (i) (2x+3y)^(3) " " (ii) (5y-3x)^(3) " " (iii) (2a+3b)...

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  7. Evaluate (2x-3y+5)^(3).

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  8. If a+2b=5, then show that a^(3)+8b^(3)+30ab=125.

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  9. If 2x-3y=10 and xy=16, find the value of 8x^(3)-27y^(3).

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  10. Evaluate : (i) (98)^(3) " " (ii) (598)^(3) " " (iii) (1003)^(3)

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  11. Factorise : (i) 4a^(2)+9b^(2)+16c^(2)+12ab-24bc-16ca (ii) (4)/(9)x...

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  12. Verify : (i) x^(3)+y^(3)=(x+y)(x^(2)-xy+y^(2)) " " (ii) x^(3)-y^(...

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  13. Factorise : (i) 9a^(3)-27b^(3) " " (ii) a^(3)-343 " " (iii) a^(...

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  14. Find the product : (i) (x+3)(x^(2)-3x+9) " " (ii) (7+5b)(49-35b+2...

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  15. Factorise : (i) a^(3)+27b^(3)+8c^(3)-18abc " " (ii) 2sqrt(2)a^(3)...

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  16. Find the product : (i) (a+2b+4c)(a^(2)+4b^(2)+16c^(2)-2ab-8bc-4ca) ...

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  17. Factorise : (i) (x-y)^(3)+(y-z)^(3)+(z-x)^(3) (ii) (x-2y)^(3)+(2y-...

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  18. Without actually calculating the cube find the value of the following ...

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

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  20. If x+y+z=0show that x^3+y^3+z^3=3x y z.

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