Question

What are the factors of (z-y) ^3 + (y - z) ^3 +(z-x) ^3?
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Answer 1

Answer:

3, (x-y), (y-z), (z-x) are the factors.

Step-by-step explanation:

We know that

${a}^{3} + {b}^{3} + {c}^{3} - 3abc \: = (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca)$

$if \: a + b + c = 0 \: then$

${a}^{3} + {b}^{3} + {c}^{3} = 3abc$

Now taking x-y = a,y-z = b , z-x = c we get

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

Therefore using the above equation

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