Упр.101 Вариант 3 Дидактические материалы ГДЗ Мерзляк Полонский 8 класс (Алгебра)

1) (v45+v180)•v5;
2) (6v2-3v50+v72)•v2;
3) (4-v6)(2+3v6);
4) (2v7-v2)(v7+6v2);
5) (v19-v13)(v19+v13);
6) (6vm+8vn)(6vm-8vn);
7) (v3+2)^2;
8) (2v6-3v7)^2.

1. $$\left(\sqrt{45}+\sqrt{180}\right)\cdot\sqrt{5}=\left(\sqrt{9\cdot 5}+\sqrt{36\cdot 5}\right)\cdot\sqrt{5}$$
   $$=(3\sqrt{5}+6\sqrt{5})\cdot\sqrt{5}=9\sqrt{5}\cdot\sqrt{5}=9\cdot 5=45.$$
2. $$\left(6\sqrt{2}-3\sqrt{50}+\sqrt{72}\right)\cdot\sqrt{2}=\left(6\sqrt{2}-3\sqrt{25\cdot 2}+\sqrt{36\cdot 2}\right)\cdot\sqrt{2}$$
   $$=\left(6\sqrt{2}-15\sqrt{2}+6\sqrt{2}\right)\cdot\sqrt{2}=(-3\sqrt{2})\cdot\sqrt{2}=-3\cdot 2=-6.$$
3. $$\left(4-\sqrt{6}\right)\left(2+3\sqrt{6}\right)=8+12\sqrt{6}-2\sqrt{6}-3\sqrt{36}$$
   $$=8+10\sqrt{6}-18=10\sqrt{6}-10.$$
4. $$\left(2\sqrt{7}-\sqrt{2}\right)\left(\sqrt{7}+6\sqrt{2}\right)=2\sqrt{7}\cdot\sqrt{7}+12\sqrt{14}-\sqrt{14}-6\sqrt{2}\cdot\sqrt{2}$$
   $$=14+11\sqrt{14}-12=2+11\sqrt{14}.$$
5. $$\left(\sqrt{19}-\sqrt{13}\right)\left(\sqrt{19}+\sqrt{13}\right)=19-13=6.$$
6. $$\left(6\sqrt{m}+8\sqrt{n}\right)\left(6\sqrt{m}-8\sqrt{n}\right)=\left(6\sqrt{m}\right)^2-\left(8\sqrt{n}\right)^2$$
   $$=36m-64n.$$
7. $$\left(\sqrt{3}+2\right)^2=3+4\sqrt{3}+4=7+4\sqrt{3}.$$
8. $$\left(2\sqrt{6}-3\sqrt{7}\right)^2=4\cdot 6-2\cdot 2\sqrt{6}\cdot 3\sqrt{7}+9\cdot 7$$
   $$=24-12\sqrt{42}+63=87-12\sqrt{42}.$$

Ответ

1) $$45$$; 2) $$-6$$; 3) $$10\sqrt{6}-10$$; 4) $$2+11\sqrt{14}$$; 5) $$6$$; 6) $$36m-64n$$; 7) $$7+4\sqrt{3}$$; 8) $$87-12\sqrt{42}$$.