Question

Heya,

Factorise,

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

Need accurate answer!! :)

Answer 1

ello


plz refer the given attachment



thanks a lot anku di

Answer 2

Given Equation is a^3(b - c) + b^3(c - a) + c^3(a - b).

Now,

This equation can be written as :

(a(b-c))^3 + (b(c-a))^3 + (c(a - b))^3.


Now,

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

               = ab - ac + bc - ba + ca - cb

               = 0.



We know that when a + b + c = 0 then a^3 + b^3 + c^3 = 3abc.

Therefore,

(a(b - c))^3 + (b(c - a))^3 + (c(a - b))^3 = 3(a(b - c))(b(c-a))(c(a-b))

                                                            = 3abc(b-c)(c-a)(a-b).



Hope this helps!