Упр.356 ГДЗ Мерзляк Полонский 7 класс (Алгебра)

1) 6a; 3) -9a^4 b^5; 5) 1/8 x^3 y^6;
2) 3b^2; 4) -0,2m^8 n^9; 6) -5/7 ab^2 c^8. Выполните умножение:
1) 3х(4х2 — х);
2) -5а2(а2 -6а-3);
3) (8b2 -10b + 2) * 0,5b;
4) х3(х5 — х2 + 7х -1);
5) -2c2d4 (4с2 — c3d + bd4);
6) (5m3n — 8mn2 — 2n6) * (-4m2n8).

1. $$\left(6a\right)^2=36a^2$$
   $$\left(3b^2\right)^2=9b^4$$
   $$\left(-9a^4b^5\right)^2=81a^8b^{10}$$
   $$\left(-0{,}2m^8n^9\right)^2=0{,}04m^{16}n^{18}$$
   $$\left(\frac18x^3y^6\right)^2=\frac1{64}x^6y^{12}$$
   $$\left(-\frac57ab^2c^8\right)^2=\frac{25}{49}a^2b^4c^{16}$$
2. $$3x(4x^2-x)=12x^3-3x^2$$
   $$-5a^2(a^2-6a-3)=-5a^4+30a^3+15a^2$$
   $$\left(8b^2-10b+2\right)\cdot0{,}5b=4b^3-5b^2+b$$
   $$x^3(x^5-x^2+7x-1)=x^8-x^5+7x^4-x^3$$
   $$-2c^2d^4(4c^2-c^3d+5d^4)=-8c^4d^4+2c^5d^5-10c^2d^8$$
   $$\left(5m^3n-8mn^2-2n^6\right)\cdot(-4m^2n^8)=-20m^5n^9+32m^3n^{10}+8m^2n^{14}$$

Ответ

1) $$36a^2,\ 9b^4,\ 81a^8b^{10},\ 0{,}04m^{16}n^{18},\ \frac1{64}x^6y^{12},\ \frac{25}{49}a^2b^4c^{16}$$

2) $$12x^3-3x^2,\ -5a^4+30a^3+15a^2,\ 4b^3-5b^2+b,\ x^8-x^5+7x^4-x^3,\ -8c^4d^4+2c^5d^5-10c^2d^8,\ -20m^5n^9+32m^3n^{10}+8m^2n^{14}$$