Question

simplify.this question​

Answer 1

Answer:

We use the fact that if a+b+c = 0, then a^3+b^3+c^3 = 3 abc

(a^2 - b^2)+( b^2-c^2)+ (c^2-a^2)= 0

also (a-b)+(b-c)+(c-a)=0

we assume that a not equal to b not equal to c

Hence,

(a^2-b^2)^3+ (b^2-c^2)^3+ (c^2-a^2)^3 ÷ (a-b)^3 +(b-c)^3 +(c-a)^3

=3(a^2-b^2) (b^2-c^2) (c^2-a^2) / [3 (a-b) (b-c) (c-a)]

= (a+b) (b+c) (c+a)

So, a^2-b^2 = (a+b) (a-b)

Hope this helped you