Question

Factorize: (a – b)3
+ (b – c)3

+ (c – a)3

Answer 1

We know that if

a+b+c=0

a³+b³+c³=3abc

So,

a-b+b-c+c-a=0

Therefore, (a-b)³+(b-c)³+(c-a)³=3(a-b)(b-c)(c-a)

Answer 2

Answer:

(a-b)3 + (b-c)3 + (c-a)3 = a3 - b3 - 3ab(a-b) + b3 - c3 - 3bc(b-c) + c3 - a3 - 3ca(c-a)

= - 3a2b + 3ab2 - 3b2c + 3bc2 - 3ac2 + 3 a2c = 3 (- a2b + ab2 - b2c + bc2 - ac2 + a2c)

= 3 [(a2(c-b) + (b2(a-c) + (c2(b-a)]

hope its helpfull for u