Question

Factorise 8(a+b+c)^3-(b+c)^3-(c + a)^3-(a+b)^3

Answer 1

(a-b)³+(b-c)³+(c-a)³

=(a³-3a²b+3ab²+b³)+(b³-3a²b+3ab²-c³)+(c³-3a²b+3ab²-a³)

= -3a²b+3ab²-3b²c+3bc²-3c²a+3ac²

= 3a²(c-b)+3b²(a-c)+3c²(b-a)