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If x+y +z=0, then (x+y) (y+z) (z+x) is ...

If `x+y +z=0`, then `(x+y) (y+z) (z+x)` is equal to which of the following:

A

`-xyz`

B

`x^(2)+y^(2)+z^(3)`

C

`x^(3)+y^(3) +z^(3)+3xyz`

D

xyz

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Verified by Experts

The correct Answer is:
A
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LUCENT PUBLICATION-ALGEBRAIC IDENTITIES -Exercise - 1A
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  2. What is the LCM of (6x^(3) +60x^(2) +150x) and (3x^(4) +12 x^(3) -15 x...

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  3. If HCF of (x^(2)+x-12) and (2x^(2)-kx -9) is (x-k), then value of k i...

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  4. What is the HCF of (x^(2) +bx -x -b) and [x^(2) +x (a-1)-a] ?

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  5. If 3x^(3) -2x^(2)y -13xy^(2)+10y^(3) is divided by x-2y, then what wil...

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  6. When x^3 + 5x^2 +10k is divided by (x^2+2) the remainder obtained is ...

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  7. If (5x^(2)+14x +2)^(2)-(4x^(2) -5x +7)^(2) is divided by x^(2)+x+1, th...

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  8. What are the components of (x^(29) -x^(24) +x^(13) -1)?

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  9. If x^(2)-4x +1=0, then what is the value of x^(3)+(1)/(x^(3)) ?

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  10. If x+y+z=6 and xy+yz +zx =11 then what is the vlaue of x^(3) +y^(3)+z^...

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  11. If a is a rational number such that (x-a) is a factor of x^(3)-3x^(2)-...

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  12. If x^(2) -11x +a and x^(2) -14 x +2a have a common factor then what ar...

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  13. For what value of k, HCF of 2x^(2)+kx -12 and x^(2) +x-2k -2 is (x+4).

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  14. What is x(y - z) (y + z) + y(z - x) (z + x) + z(x - y) (x + y) equal t...

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  15. If (x//y) = (z//w), then what is (xy + zw)^2 equal to ?

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  16. If 1/(x + 1) + 2/(y + 2) + (1009)/(z + 1009) = 1 then what is the valu...

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  17. If a = 258, b=260 and c=262 then value of a^(3) +b^(3) +c^(3) -3abc is

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  18. If the HCF of x^(3) - 27 and x^(3) + 4x^(2) + 12x + k is a quadratic p...

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  19. When x^(40)+2 is divided by x^(4)+1, then what is the remainder?

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  20. If a^(x) =b^(y) =c^(z) and abc =1 then xy+yz+zx is equal to which of...

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