Упр.101 Вариант 2 Дидактические материалы ГДЗ Мерзляк Полонский 8 класс (Алгебра)

1) (v63-v28)•v7;
2) (7v3+v48-v75)•v3;
3) (6-v5)(2+7v5);
4) (5v2+6v3)(6v2-5v3);
5) (v17-v11)(v17+v11);
6) (2vx-5vy)(2vx+5vy);
7) (v6-2)^2;
8) (3v7-2v3)^2.

1. $$\left(\sqrt{63}-\sqrt{28}\right)\cdot \sqrt{7}=\left(\sqrt{9\cdot 7}-\sqrt{4\cdot 7}\right)\cdot \sqrt{7}$$
   $$=(3\sqrt{7}-2\sqrt{7})\cdot \sqrt{7}=\sqrt{7}\cdot \sqrt{7}=7.$$
2. $$\left(7\sqrt{3}+\sqrt{48}-\sqrt{75}\right)\cdot \sqrt{3}=\left(7\sqrt{3}+4\sqrt{3}-5\sqrt{3}\right)\cdot \sqrt{3}$$
   $$=6\sqrt{3}\cdot \sqrt{3}=6\cdot 3=18.$$
3. $$\left(6-\sqrt{5}\right)\left(2+7\sqrt{5}\right)=12+42\sqrt{5}-2\sqrt{5}-7\cdot 5$$
   $$=12+40\sqrt{5}-35=40\sqrt{5}-23.$$
4. $$\left(5\sqrt{2}+6\sqrt{3}\right)\left(6\sqrt{2}-5\sqrt{3}\right)=30\cdot 2-25\sqrt{6}+36\sqrt{6}-30\cdot 3$$
   $$=60+11\sqrt{6}-90=11\sqrt{6}-30.$$
5. $$\left(\sqrt{17}-\sqrt{11}\right)\left(\sqrt{17}+\sqrt{11}\right)=\left(\sqrt{17}\right)^2-\left(\sqrt{11}\right)^2$$
   $$=17-11=6.$$
6. $$\left(2\sqrt{x}-5\sqrt{y}\right)\left(2\sqrt{x}+5\sqrt{y}\right)=\left(2\sqrt{x}\right)^2-\left(5\sqrt{y}\right)^2$$
   $$=4x-25y.$$
7. $$\left(\sqrt{6}-2\right)^2=\left(\sqrt{6}\right)^2-2\cdot \sqrt{6}\cdot 2+2^2$$
   $$=6-4\sqrt{6}+4=10-4\sqrt{6}.$$
8. $$\left(3\sqrt{7}-2\sqrt{3}\right)^2=\left(3\sqrt{7}\right)^2-2\cdot 3\sqrt{7}\cdot 2\sqrt{3}+\left(2\sqrt{3}\right)^2$$
   $$=9\cdot 7-12\sqrt{21}+4\cdot 3=63-12\sqrt{21}+12=75-12\sqrt{21}.$$

Ответ

1) $$7$$; 2) $$18$$; 3) $$40\sqrt{5}-23$$; 4) $$11\sqrt{6}-30$$; 5) $$6$$; 6) $$4x-25y$$; 7) $$10-4\sqrt{6}$$; 8) $$75-12\sqrt{21}$$.