Упр.875 ГДЗ Никольский Потапов 9 класс (Алгебра)

б) (v8-3v2+v10)(v2+v5)-2v5+v10-5v2.

а)

$$ (2\sqrt{3}-3\sqrt{2}+\sqrt{6})(\sqrt{6}-\sqrt{2}-2\sqrt{3})+8\sqrt{3}-4\sqrt{6} $$
$$ =2\sqrt{18}-2\sqrt{6}-4\sqrt{9}-3\sqrt{12}+3\sqrt{4}+6\sqrt{6}+\sqrt{36}-\sqrt{12}-2\sqrt{18}+8\sqrt{3}-4\sqrt{6} $$
$$ =-4\sqrt{9}-4\sqrt{12}+3\sqrt{4}+\sqrt{36}+8\sqrt{3} $$
$$ =-4\cdot 3-4\cdot 2\sqrt{3}+3\cdot 2+6+8\sqrt{3} $$
$$ =-12-8\sqrt{3}+6+6+8\sqrt{3}=0. $$

б)

$$ (\sqrt{8}-3\sqrt{2}+\sqrt{10})(\sqrt{2}+\sqrt{5})-2\sqrt{5}+\sqrt{10}-5\sqrt{2} $$
$$ =\sqrt{16}+\sqrt{40}-3\sqrt{4}-3\sqrt{10}+\sqrt{20}+\sqrt{50}-2\sqrt{5}+\sqrt{10}-5\sqrt{2} $$
$$ =4+2\sqrt{10}-3\cdot 2-3\sqrt{10}+2\sqrt{5}+5\sqrt{2}-2\sqrt{5}+\sqrt{10}-5\sqrt{2} $$
$$ =4-6=-2. $$

Ответ

а) $$0$$; б) $$-2$$.