Factors of 27 x 3- y 3- z 3-9 xyz are-A- 3 x-y-z9 x2-y2-z2-3 x y-y z-3 x zB- 3 x-y-z9 x2-y2-z2-3 x y-y z-3 x zC- 3 x-y-z9 x2-y2-z2-3 x y-y z-3 x zD- 3 x-y-z9 x2-y2-z2-3 x y-y z-3 x z

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Factorisation using algebraic identities

Factors of 27...

Question

Factors of $27 x^{3} + y^{3} + z^{3} - 9 x y z$ are:

(3 x + y + z) (9 x^{2} + y^{2} + z^{2} - 3 x y - y z - 3 x z)

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(3 x + y + z) (9 x^{2} + y^{2} + z^{2} + 3 x y + y z + 3 x z)

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(3 x - y + z) (9 x^{2} + y^{2} - z^{2} + 3 x y + y z + 3 x z)

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(3 x - y - z) (9 x^{2} + y^{2} + z^{2} - 3 x y - y z - 3 x z)

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Solution

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27 x^{3} + y^{3} + z^{3} - 9 x y z

= (3 x + y + z) [(9 x^{2} + y^{2} + z^{2} - 3 x y - y z - 3 z x)]

x^{3} + y^{3} + z^{3} - 3 x y z = (x + y + z) (x^{2} + y^{2} + z^{2} - x y - y z - z x)

x^{2} + y^{2} + z^{2} - x y - y z - z x = \frac{1}{2} [(x - y)^{2} + (y - z)^{2} + (z - x)^{2}]

2 y^{2} + 3 y z, - y^{2} - y z - z^{2}

y z + 2 z^{2}

3 y^{2} - z^{2}

- y^{2} + y z + z^{2}

If $(x^{2} + y^{2} + z^{2}) = (x y + y z + z x)$ , $what is the value of x^{3} + y^{3} + z^{3}$ ?

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