Answer:
[tex]=10\sqrt{10}+10\sqrt{2}-10\sqrt{5}-10[/tex]
Step-by-step explanation:
[tex](2\sqrt{5} -\sqrt{10})(5\sqrt{2}+\sqrt{10})[/tex]
[tex]=2\sqrt{5}\cdot5\sqrt{2}+2\sqrt{5}\sqrt{10}-5\sqrt{2}\sqrt{10}-\sqrt{10}\sqrt{10}[/tex]
[tex]=10\sqrt{10}+2\sqrt{50}-5\sqrt{20}-10[/tex]
[tex]=10\sqrt{10}+2\sqrt{25 \cdot 2}-5\sqrt{4 \cdot5}-10[/tex]
[tex]=10\sqrt{10}+2\sqrt{25}\sqrt{2}-5\sqrt{4}\sqrt{5}-10[/tex]
[tex]=10\sqrt{10}+2\cdot5\sqrt{2}-5\cdot2\sqrt{5}-10[/tex]
[tex]=10\sqrt{10}+10\sqrt{2}-10\sqrt{5}-10[/tex]
