Question

factorize (a power 2 -b power 2) whole power 3 +(b power 2 - c power 2 ) whole power 3 = (c power 2 - a power 2 ) whole power 3

Answer 1

$(a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3\\\\here \ a^2-b^2+b^2-c^2+c^2-a^2=0\\\\ If \ a+b+c=0 \ then \ a^3+b^3+c^3=3abc\\\\Thus \\\\\bf(a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3\\\\=3(a^2-b^2)(b^2-c^2)(c^2-a^2)\\\\=3(a-b)(b-c)(c-a)(a+b)(b+c)(c+a)$