Find the value of ${(x - y)}^{3} + {(y - z)}^{3} + {(z - x)}^{3}$

Open in App

Solution

Let $a = x - y, b = y - z, c = z - x$
Here $a + b + c = x - y + y - z + z - x = 0$
Then, $a^{3} + b^{3} + c^{3} = 3 a b c$
$\Rightarrow (x - y)^{3} + (y - z)^{3} + (z - x)^{3} = 3 (x - y) (y - z) (z - x) .$

Suggest Corrections

Similar questions

x + y + z = 0

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

x = 1, y = 2

z = 5

x^{3} - y^{3} - z^{3}

x + y + z = 0

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

x + y + z = 0

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

Join BYJU'S Learning Program