Question

The value of (x-a )^3 +(x-b )^3 +(x-c )^3 -3 (x-a )(x-b )(x -c )when a +b +c =3x

Answer 1

we know that,
a³+b³+c³-3abc=(a+b+c)(a²+b²+c²-ab-bc-ca)
If a+b+c=0 then,
a³+b³+c³-3abc=0×(a²+b²+c²-ab-bc-ca)=0 .....(1)

(x-a)³+(x-b)³+(x-c)³-3(x-a)(x-b)(x-c)
let a=(x-a)
b=(x-b)
and c=(x-c)
a+b+c=x-a+x-b+x-c=3x-(a+b+c)=3x-3x=0....(as a+b+c=3x)
(x-a)³+(x-b)³+(x-c)³-3(x-a)(x-b)(x-c)=0

Thus the answer is 0....

Answer 2

answer is 0.

hope it helps.