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What is the value of ((x - y)^3 + (y - ...

What is the value of `((x - y)^3 + (y - z)^3 + (z - x)^3)/(9(x - y)(y - z)(z - x)) `?

A

`0`

B

`1/3`

C

`1/9`

D

`1`

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Knowledge Check

  • Value of (x-y)^(3) +(y-z)^(3) +(z-x)^(3) is

    A
    `3xyz `
    B
    `3(x+y) (y+z) (z+x`
    C
    `3(x-y) (y-z) (z-x)`
    D
    0

  • Evaluate the expression ((x-y)^(3) + (y-z)^(3) + (z-x)^(3) )/( (x-y) (y-z) + (z-x) ) in the simplest form.

    A
    1
    B
    2
    C
    3
    D
    `-1`

  • The value of ( x + y + z)^(3) - ( y + z - x )^(3) - ( z - x - y )^(3) - ( x + y - z) ^(3) is

    A
    12 xyz
    B
    24 xyz
    C
    36 xyz
    D
    0

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