Упр.387 ГДЗ Колягин Ткачёва 7 класс (Алгебра)

1) (-1 3/5 x^3 y^2 ) (-1/2 c^2 x^2 )^3;
2) (2 1/4 x^3 y) (2/3 xy^2 )^2;
3) (-3bc^2 )^3 (2ab^2 )^2;
4) (-2a^2 b)^2 (-a^2 b^3 )^3;
5) (5/6 m^2 n)^2 (6mn^2 )^2;
6) (3/7 m^3 n)^2 (-7mn^2 )^3.
Найти значение выражения:
1) 5m^2-10mn+5n^2 при m=142; n=42;
2) 6m^2+12mn+6n^2 при m=56; n=44;
3) -36a^3+4a^2 b-1/9 ab^2 при a=4; b=48;
4) -64a^3-8a^2 b-1/4 ab^2 при a=-6; b=84.

1. $$\left(-1\frac{3}{5}x^3y^2\right)\left(-\frac12c^2x^2\right)^3$$
   $$=-\frac85x^3y^2\cdot\left(-\frac18c^6x^6\right)$$
   $$=\frac15x^9y^2c^6$$
2. $$\left(2\frac14x^3y\right)\left(\frac23xy^2\right)^2$$
   $$=\frac94x^3y\cdot\frac49x^2y^4$$
   $$=x^5y^5$$
3. $$(-3bc^2)^3(2ab^2)^2$$
   $$=-27b^3c^6\cdot4a^2b^4$$
   $$=-108a^2b^7c^6$$
4. $$(-2a^2b)^2(-a^2b^3)^3$$
   $$=4a^4b^2\cdot(-a^6b^9)$$
   $$=-4a^{10}b^{11}$$
5. $$\left(\frac56m^2n\right)^2(6mn^2)^2$$
   $$=\frac{25}{36}m^4n^2\cdot36m^2n^4$$
   $$=25m^6n^6$$
6. $$\left(\frac37m^3n\right)^2(-7mn^2)^3$$
   $$=\frac{9}{49}m^6n^2\cdot(-343m^3n^6)$$
   $$=-63m^9n^8$$

2. $$5m^2-10mn+5n^2=5(m^2-2mn+n^2)=5(m-n)^2$$
   $$=5(142-42)^2=5\cdot100^2=50000$$
3. $$6m^2+12mn+6n^2=6(m^2+2mn+n^2)=6(m+n)^2$$
   $$=6(56+44)^2=6\cdot100^2=60000$$
4. $$-36a^3+4a^2b-\frac19ab^2=-a\left(36a^2-4ab+\frac19b^2\right)$$
   $$=-a\left(6a-\frac13b\right)^2$$
   $$=-4\left(6\cdot4-\frac13\cdot48\right)^2=-4(24-16)^2=-4\cdot8^2=-256$$
5. $$-64a^3-8a^2b-\frac14ab^2=-a\left(64a^2+8ab+\frac14b^2\right)$$
   $$=-a\left(8a+\frac12b\right)^2$$
   $$=-(-6)\left(8\cdot(-6)+\frac12\cdot84\right)^2$$
   $$=6(-48+42)^2=6\cdot(-6)^2=6\cdot36=216$$

Ответ

1) $$\frac15x^9y^2c^6$$; 2) $$x^5y^5$$; 3) $$-108a^2b^7c^6$$; 4) $$-4a^{10}b^{11}$$; 5) $$25m^6n^6$$; 6) $$-63m^9n^8$$.
Значения выражений: 1) $$50000$$; 2) $$60000$$; 3) $$-256$$; 4) $$216$$.