Упр.17.13 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) (-3m+7n)^2; 2) (-0,4x-1,5y)^2;
3) (-x^2-y)^2; 4) (-a^2 b^2+c^10 )^2.

1. $$(-3m+7n)^2=(7n-3m)^2$$
   $$=(7n)^2-2\cdot 7n\cdot 3m+(3m)^2$$
   $$=49n^2-42mn+9m^2.$$
2. $$(-0,4x-1,5y)^2=(0,4x+1,5y)^2$$
   $$=(0,4x)^2+2\cdot 0,4x\cdot 1,5y+(1,5y)^2$$
   $$=0,16x^2+1,2xy+2,25y^2.$$
3. $$(-x^2-y)^2=(x^2+y)^2$$
   $$=(x^2)^2+2\cdot x^2\cdot y+y^2$$
   $$=x^4+2x^2y+y^2.$$
4. $$(-a^2b^2+c^{10})^2=(c^{10}-a^2b^2)^2$$
   $$=(c^{10})^2-2\cdot c^{10}\cdot a^2b^2+(a^2b^2)^2$$
   $$=c^{20}-2a^2b^2c^{10}+a^4b^4.$$

Ответ

$$1)\ 49n^2-42mn+9m^2;$$
$$2)\ 0,16x^2+1,2xy+2,25y^2;$$
$$3)\ x^4+2x^2y+y^2;$$
$$4)\ c^{20}-2a^2b^2c^{10}+a^4b^4.$$