[tex](a+b)^2=a^2+2ab+b^2\\\\\[(\sqrt{2})^3+(\sqrt{5})^3]^2=\\=[2\sqrt{2}+5\sqrt{5}]^2=\\=(2\sqrt{2})^2+2\cdot2\cdot5\sqrt{2\cdot5}+(5\sqrt{5})^2=\\=4\cdot2+20\sqrt{10}+25\cdot5=\\=8+20\sqrt{10}+125=\\=\boxed{133+20\sqrt{10}}[/tex]
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[tex](a+b)^2=a^2+2ab+b^2\\\\\[(\sqrt{2})^3+(\sqrt{5})^3]^2=\\=[2\sqrt{2}+5\sqrt{5}]^2=\\=(2\sqrt{2})^2+2\cdot2\cdot5\sqrt{2\cdot5}+(5\sqrt{5})^2=\\=4\cdot2+20\sqrt{10}+25\cdot5=\\=8+20\sqrt{10}+125=\\=\boxed{133+20\sqrt{10}}[/tex]