Задание 10 Параграф 16 ГДЗ Рабочая тетрадь 1 Мерзляк Полонский 7 класс (Алгебра)

1) (-7a+2b)^2;
2) (-3x-5y)^2;
3) (-0,6m-20n^2 )^2;
4) (-2a^3+1/12 b^4 )^2.

1. $$(-7a+2b)^2=(-7a)^2+2\cdot(-7a)\cdot 2b+(2b)^2$$
   $$=49a^2-28ab+4b^2.$$
2. $$(-3x-5y)^2=(-3x)^2+2\cdot(-3x)\cdot(-5y)+(-5y)^2$$
   $$=9x^2+30xy+25y^2.$$
3. $$(-0{,}6m-20n^2)^2=(-0{,}6m)^2+2\cdot(-0{,}6m)\cdot(-20n^2)+(20n^2)^2$$
   $$=0{,}36m^2+24mn^2+400n^4.$$
4. $$\left(-2a^3+\frac{1}{12}b^4\right)^2=(-2a^3)^2+2\cdot(-2a^3)\cdot\frac{1}{12}b^4+\left(\frac{1}{12}b^4\right)^2$$
   $$=4a^6-\frac{1}{3}a^3b^4+\frac{1}{144}b^8.$$

Ответ

1) $$49a^2-28ab+4b^2$$
2) $$9x^2+30xy+25y^2$$
3) $$0{,}36m^2+24mn^2+400n^4$$
4) $$4a^6-\frac{1}{3}a^3b^4+\frac{1}{144}b^8$$