Упр.357 ГДЗ Мерзляк Полонский 7 класс (Алгебра)

1) 2b; 3) 1/3 x^5; 5) -1/4 x^3 y^2;
2) 10c^4; 4) -0,1m^7 n^10; 6) -a^3 b^2 c. Упростите выражение:
1) 8x — 2х(3х + 4);
2) 7а2 +3a(9-5a);
3) 6х(4х-7)-12(2х2 +1);
4) с (с2 — 1) + с2(с — 1);
5) 2m(m — 3n) + m(5m + 11n);
6) 8х (х2 + у2)- 9х (х2 — у2);
7) 5b3(2b — 3) — 2,5b3(4b — 6);
8) х (5х2 + 6x + 8) — 4х (2 + 2х + х2).

1. $$ (2b)^3 = 2^3b^3 = 8b^3 $$
   $$ (10c^4)^3 = 10^3c^{12} = 1000c^{12} $$
   $$ \left(\frac{1}{3}x^5\right)^3 = \frac{1}{27}x^{15} $$
   $$ (-0{,}1m^7n^{10})^3 = -0{,}001m^{21}n^{30} $$
   $$ \left(-\frac{1}{4}x^3y^2\right)^3 = -\frac{1}{64}x^9y^6 $$
   $$ (-a^3b^2c)^3 = -a^9b^6c^3 $$
2. $$ 8x — 2x(3x + 4) = 8x — 6x^2 — 8x = -6x^2 $$
   $$ 7a^2 + 3a(9 — 5a) = 7a^2 + 27a — 15a^2 = -8a^2 + 27a $$
   $$ 6x(4x — 7) — 12(2x^2 + 1) = 24x^2 — 42x — 24x^2 — 12 = -42x — 12 $$
   $$ c(c^2 — 1) + c^2(c — 1) = c^3 — c + c^3 — c^2 = 2c^3 — c^2 — c $$
   $$ 2m(m — 3n) + m(5m + 11n) = 2m^2 — 6mn + 5m^2 + 11mn = 7m^2 + 5mn $$
   $$ 8x(x^2 + y^2) — 9x(x^2 — y^2) = 8x^3 + 8xy^2 — 9x^3 + 9xy^2 = -x^3 + 17xy^2 $$
   $$ 5b^3(2b — 3) — 2{,}5b^3(4b — 6) = 10b^4 — 15b^3 — 10b^4 + 15b^3 = 0 $$
   $$ x(5x^2 + 6x + 8) — 4x(2 + 2x + x^2) = 5x^3 + 6x^2 + 8x — 8x — 8x^2 — 4x^3 = x^3 — 2x^2 $$

Ответ

1) $$8b^3,\ 1000c^{12},\ \frac{1}{27}x^{15},\ -0{,}001m^{21}n^{30},\ -\frac{1}{64}x^9y^6,\ -a^9b^6c^3$$
2) $$-6x^2,\ -8a^2+27a,\ -42x-12,\ 2c^3-c^2-c,\ 7m^2+5mn,\ -x^3+17xy^2,\ 0,\ x^3-2x^2$$