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

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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Verify that x3+y3+z3-3xyz=1/2(x+y+z)[(x-y)2+(y-z)2+(z-x)2]

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

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

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

For any scalar p prove that =|[x,x^2, 1+p x^3],[y, y^2, 1+p y^3],[z, z^2 ,1+p z^3]|=(1+p x y z)(x-y)(y-z)(z-x) .

Show that : |[x, y, z ],[x^2,y^2,z^2],[x^3,y^3,z^3]|=x y z(x-y)(y-z)(z-x)dot

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

Prove that : Det[[x,x^2,x^3],[y,y^2,y^3],[z,z^2,z^3]]=xyz(x-y)(y-z)(z-x)

Prove that [(x^2+y^2+z^2)/(x+y+z)]^(x+y+z)> x^x y^y z^z >[(x+y+z)/3]^(x+y+z)(x ,y ,z >0)

Simplify: ((x^(2)-y^(2))^(3) + (y^(2) - z^(2))^(3) + (z^(2) -x^(2))^(3))/((x-y)^(3) + (y-z)^(3) + (z-x)^(3))

NAGEEN PRAKASHAN ENGLISH-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 : 4a^(2)+9b^(2)+16c^(2)+12ab-24bc-16ca

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