Question

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

Answer 1

Hi,

We know the identity
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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)

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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 )

I hope this will useful to you.

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Answer 2

Answer

Hope this answer helps you