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Algebraic Identity (a-b)^3

If x=10, y=-4...

Question

$I f x = 10, y = - 4, z = - 6, x^{3} + y^{3} + z^{3} =$ .

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Solution

$i f x + y + z = 0, t h e n x^{3} + y^{3} + z^{3} = 3 x y z$

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x + y + z = 0

, what can be said about

x^{3} + y^{3} + z^{3}

?

If $x + y + z = 0$
then $x^{3} + y^{3} + z^{3}$ =___?

Q. If x + y + z = 0, then (x + y)³+ (y + z)³ + (z + x)³ = ________.

Q. Prove that:

(x + y)³+ (y + z)³+ (z + x)³ − 3(x + y) (y + z) (z + x) = (x³ + y³ + z³ − 3xyz).

x^{3} + y^{3} + z^{3} = 3 x y z

x + y + z = ?

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