Question

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

Answer 1

Hi,

We know the identity

********************************************

i) x ^3 + y^3 + y^3 = (x + y + z)

(x^2 + y ^2 + z^2 - xy - yz - zx ) + 3xyz

* If x + y + z = 0

then

x^3 + y^3 + z^3 = 3xyz ------(1)

*******************************************

Now according to the problem ,

Let

x = a - b ;

y = b- c ;

z = c - a ;

x + y + z = a - b + b - c + c - a = 0

Therefore,

Using ( 1 )

x ^3 + y ^3 + z ^3 = 3xyz

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

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