Answer
$2x^{2}+x\sqrt[3]{y^{2}}-y\sqrt[3]{y}$
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).
$F:\quad x\times 2x=2x^{2}$
$O:\quad x\times(-\sqrt[3]{y^{2}})=-x\sqrt[3]{y^{2}}$
$I:\quad \sqrt[3]{y^{2}}\times 2x=2x\sqrt[3]{y^{2}}$
$L:\quad \sqrt[3]{y^{2}}\times(-\sqrt[3]{y^{2}})=-\sqrt[3]{y^{3}\times y}=-\sqrt[3]{y^{3}}\times\sqrt[3]{y}=-y\sqrt[3]{y}$
Add the terms (O and I are like terms...)
$...$= $2x^{2}+x\sqrt[3]{y^{2}}-y\sqrt[3]{y}$
