Question

(X-a)^3+(x-b)^3+(x-c)^3-3(x-a)(x-b)(x-c) when a+b+c =3x

Answer 1

Answer:

a³+b³+c³ - 3abc = (a+b+c)(a²+b²+c²-ab-bc-ca)

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

= (x-a+x-b+x-c) [(x-a)² +(x-b)²+ (x-c)² -(x-a)(x-b) -(x-b)(x-c)-(x-c)(x-a)]

= [ 3x -(a+b+c)] [(x-a)² +(x-b)²+ (x-c)² -(x-a)(x-b) -(x-b)(x-c)-(x-c)(x-a)]

= (3x-3x)[(x-a)² +(x-b)²+ (x-c)² -(x-a)(x-b) -(x-b)(x-c)-(x-c)(x-a)]

=0

Hope this helps. Happy learning!!!