Question

factorise (x-y)^3 - (y-z)^3 - (z-x)^3, please send it's urgent...​

Answer 1

Answer:

Step-by-step explanation:

Given  

factorise (x-y)^3 - (y-z)^3 - (z-x)^3, please send it's urgent...

ANSWER

 We know that  

a^3 + b^3 + c^3 – 3 abc = (a + b + c)(a^2 + b^2 + c^2 – ab – bc – ac)

Let a = x – y , b = y – z and c = z – x

So substituting we get

(x – y)^3 + (y – z)^3 + (z – x)^3 – 3 (x – y)(y – z) (z – x)  

= (x – y + y – z + z – x){(x – y)^2 + (y – z)^2 + (z – x)^2 – (x – y)(y – z) – (y – z)(z – x) – (x – y)(z – x)}

= 0

So we get

 (x – y)^3 + (y – z)^3 + (z – x)^3 =  3 (x – y)(y – z) (z – x)