Factorise ${(x - y)}^{3}$ + ${(y - z)}^{3}$ + ${(z - x)}^{3}$

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Solution

Let (x - y) = a, (y - z) = b and (z - x) = c
$∵$ a + b + c = (x - y) + (y -z) + (z -x) = 0

Using identity, a+b+c = 0 ⇒ a³ + b³ + c³ = 3abc

$∴$ (x - y)³ + (y - z)³ + (z - x)³ = 3(x -y)(y - z)(z - x)

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