Question

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

Answer 1

Heya,

if a+b+c = 0Then a +b +c = 3abcNow,(a -b ) +(b -c ) +(c -a )= a -b +b -c +c -a = 0That means we can use this formula here because a+b+c is coming out to be zero(a -b ) +(b -c ) +(c -a ) = 3(a -b )(b -c )(c -a )Now let's solve the Denominator
(a-b) + (b-c) +(c-a) = 3(a-b) (b-c) (c-a)Now we have the following fraction=3(a -b )(b -c )(c -a ) /3(a-b) (b-c) (c-a)= We know that a -b = (a+b)(a-b), now we have= (a-b)(a+b)(b-c)(b+c) (c+a)(c-a) /(a-b)(b-c)(c-a)We are now left with (a+b)(b+c)(c+a) which is the answer