(a^(1/3)+a^(-1/3) ) (a^(2/3)+a^(-2/3)-1) Answer is a+1/a

Question

could not get this answer. 

Answer 1

a^(1/3)*a^(2/3) + a^(1/3)*a^(-2/3) - a^(1/3)    <---- a^(1/3) times the second polynomial

 

                                   +

 

a^(-1/3)*a^(2/3) + a^(-1/3)*a^(-2/3) - a^(-1/3) <---- a^(-1/3) times the second polynomial

 

=

 

a + a^(-1/3) - a^(1/3) + a^(1/3) + a^(-1) - a^(-1/3) =

 

a + a^(-1) <---- a^(-1/3) cancels as does a^(1/3); they are in bold and italics above, respectively

 

a + (1/a)