Factorise

${(x - y)}^{3} + {(y - z)}^{3} + {(z - x)}^{3}$ [3 MARKS]

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Solution

Formula: 1 Mark
Application: 2 Marks

Let $(x - y) = a, (y - z) = b, (z - x) = c$

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

$a + b + c = 0 \Rightarrow a^{3} + b^{3} + c^{3} = 3 a b c$

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

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Factorise

${(x - y)}^{3} + {(y - z)}^{3} + {(z - x)}^{3}$ [3 MARKS]

x + y + z = 0

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

x, y, z

\frac{x}{y} + \frac{y}{z} + \frac{z}{x} = 7

\frac{y}{x} + \frac{z}{y} + \frac{x}{z} = 9

\frac{x^{3}}{y^{3}} + \frac{y^{3}}{z^{3}} + \frac{z^{3}}{x^{3}} - 3

Simplify :

(x-y) ³ + (y-z) ³ + (z-x) ³

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