How to simplify a hard cubic root problem?

[acemi123]

Left side equal to the right side but I didn't understand the progress. Could someone explain to me, please?

 

[Deleted member 4993]

View attachment 12531
Left side equal to the right side but I didn't understand the progress. Could someone explain to me, please?

Multiply →

\(\displaystyle {\displaystyle{(5^{1/3} \ - \ 3^{1/3}) \ * \ (5^{2/3} \ + \ 15^{1/3}\ + \ 3^{2/3})}}\)

This comes from:

\(\displaystyle \displaystyle{a^3 - b^3 \ = \ (a - b) \ * \ (a^2 + ab + b^2)}\)