Mathematics
OpenStudy (saifoo.khan):

Jimmy!

OpenStudy (saifoo.khan):

jimthompson5910 (jim_thompson5910):

$\large (\sqrt[5]{4}-\sqrt[5]{2})(\sqrt[5]{125}+\sqrt[5]{8})$ $\large (\sqrt[5]{4})(\sqrt[5]{125})+(\sqrt[5]{4})(\sqrt[5]{8})+(-\sqrt[5]{2})(\sqrt[5]{125})+(-\sqrt[5]{2})(\sqrt[5]{8})$ $\large \sqrt[5]{4*125}+\sqrt[5]{4*8}-\sqrt[5]{2*125}-\sqrt[5]{2*8}$ $\large \sqrt[5]{500}+\sqrt[5]{32}-\sqrt[5]{250}-\sqrt[5]{16}$ $\large \sqrt[5]{500}+2-\sqrt[5]{250}-\sqrt[5]{16}$ $\large 2+\sqrt[5]{500}-\sqrt[5]{250}-\sqrt[5]{16}$ So $\large (\sqrt[5]{4}-\sqrt[5]{2})(\sqrt[5]{125}+\sqrt[5]{8})=2+\sqrt[5]{500}-\sqrt[5]{250}-\sqrt[5]{16}$

OpenStudy (saifoo.khan):

WOOOOOW

OpenStudy (saifoo.khan):

but that isn't in simplest form.

jimthompson5910 (jim_thompson5910):

hmm not working, ok one sec

OpenStudy (saifoo.khan):

Thanks.

jimthompson5910 (jim_thompson5910):

well none of the other terms simplify, but you could combine the second pair of terms to get $\large (\sqrt[5]{2}-1)\sqrt[5]{250}$, but that's not much of a simplification...

jimthompson5910 (jim_thompson5910):

So $\large \large (\sqrt[5]{4}-\sqrt[5]{2})(\sqrt[5]{125}+\sqrt[5]{8})=2+(\sqrt[5]{2}-1)\sqrt[5]{250}-\sqrt[5]{16}$