Answer
$2x^{2}-x\sqrt[5]{y^{3}}-y\sqrt[5]{y}$
Work Step by Step
Use the FOIL method, along with
$\sqrt[n]{a}\times\sqrt[n]{b}=\sqrt[n]{ab},\qquad$
$\sqrt[n]{a^{n}}=(\sqrt[n]{a})^{n}=a$ (for positive a).
$F:\quad x\times 2x=2x^{2}$
$O:\quad x\times(\sqrt[5]{y^{3}})=x\sqrt[5]{y^{3}}$
$I:\quad -\sqrt[5]{y^{3}}\times 2x=-2x\sqrt[5]{y^{3}}$
$L:\quad -\sqrt[5]{y^{3}}\times(\sqrt[5]{y^{3}})=-\sqrt[5]{y^{3}\times y^{3}}=-\sqrt[5]{y^{5}\times y}=-\sqrt[5]{y^{5}}\times\sqrt[5]{y}=-y\sqrt[5]{y}$
Add the terms (O and I are like terms...)
$...$= $2x^{2}-x\sqrt[5]{y^{3}}-y\sqrt[5]{y}$
