Jimmy!
\[\large (\sqrt[5]{4}-\sqrt[5]{2})(\sqrt[5]{125}+\sqrt[5]{8})\] \[\large (\sqrt[5]{4})(\sqrt[5]{125})+(\sqrt[5]{4})(\sqrt[5]{8})+(-\sqrt[5]{2})(\sqrt[5]{125})+(-\sqrt[5]{2})(\sqrt[5]{8})\] \[\large \sqrt[5]{4*125}+\sqrt[5]{4*8}-\sqrt[5]{2*125}-\sqrt[5]{2*8}\] \[\large \sqrt[5]{500}+\sqrt[5]{32}-\sqrt[5]{250}-\sqrt[5]{16}\] \[\large \sqrt[5]{500}+2-\sqrt[5]{250}-\sqrt[5]{16}\] \[\large 2+\sqrt[5]{500}-\sqrt[5]{250}-\sqrt[5]{16}\] So \[\large (\sqrt[5]{4}-\sqrt[5]{2})(\sqrt[5]{125}+\sqrt[5]{8})=2+\sqrt[5]{500}-\sqrt[5]{250}-\sqrt[5]{16}\]
WOOOOOW
but that isn't in simplest form.
hmm not working, ok one sec
Thanks.
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...
So \[\large \large (\sqrt[5]{4}-\sqrt[5]{2})(\sqrt[5]{125}+\sqrt[5]{8})=2+(\sqrt[5]{2}-1)\sqrt[5]{250}-\sqrt[5]{16} \]
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