Show that (a^(1/3) - b^(1/3)).(a^(2/3) - a^(1/3).b^(1/3) + b^(2/3)) = a - b?

Question

Please show how you worked it out, because I would like to understand how this works. So far I have tried using Binomial expansion but I got confused. Thanks

Answer 1

Your equation expands to:

            a - 2 * (a^2/3*b^1/3 - a^1/3*b^2/3) - b

so it is not a-b

Answer 2

using (x-y)(x^2+xy + y^2) = x^3 - y^3 and x = a^(1/3) and y = b^(1/3) we get

(a^(1/3) - b^(1/3)).(a^(2/3) + a^(1/3).b^(1/3) + b^(2/3)) = a - b

and what you mentioned is wrong.

with love math kp