Question

Factorise the following a cube (b - c) the whole cube +bcube (c- a ) the whole cube + c cube (a -b) the whole cube?

Answer 1

Answer:

=a^9 +b^9 +c^9 + 3*[a^6*(b-c) + b^6*(c-a) + c^6*(a-b) + a^3*(b-c)^2 + b^3*(c-a)^2 + c^3*(a-b)^2] + (b-c)^3 + (c-a)^3 +(a-b)^3

Step-by-step explanation:

[a^3*(b-c)]^3 + [b^3*(c-a)]^3 + [c^3*(a-b)]^3

= a^9 + 3*a^6*(b-c ) + 3*a^3*(b-c)^2 + (b-c)^3

+ b^9 + 3*b^6*(c-a) + 3* b^3 *(c-a)^2 + (c-a)^3

+ c^9 + 3* c^6*(a-b) + 3*c^3*(a-b)^2 + (a-b)^3

[ using the formula of (a+b)^3=a^3 + 3*a*b^2 + 3*a^2*b + b^3 ]

= a^9 +b^9 +c^9 + 3*[a^6*(b-c) + b^6*(c-a) + c^6*(a-b) + a^3*(b-c)^2 + b^3*(c-a)^2 + c^3*(a-b)^2] + (b-c)^3 + (c-a)^3 +(a-b)^3

Thank you