Question

Factorise the following.
(x - 2y) ^3 + (2y - 3z) ^3 + (3z - x) ^3
(Hint : a^3 + b^3 + c^3 = 3abc)​

Answer 1

Answer:

Step-by-step explanation:

We know that,

a3 + b3 + c3 – 3 abc = (a + b + c)(a2 + b2 + c2 -ab-bc-ca)

Also, if a + b + c = 0, then a3 + b3 + c3 = 3abc

Here, we see that (x-2y) +(2y-3z)+ (3z-x) = 0

Therefore, (x-2y)3 + (2y-3z)3 + (3z-x)3 = 3(x-2y)(2y-3z)(3z-x).