Упр.127 Вариант 2 Дидактические материалы ГДЗ Мерзляк Полонский 7 класс (Алгебра)

Используем формулу квадрата суммы и квадрата разности:

$$(u+v)^2=u^2+2uv+v^2, \qquad (u-v)^2=u^2-2uv+v^2.$$

1. $$(a+2)^2=a^2+2\cdot a\cdot 2+2^2=a^2+4a+4;$$
2. $$(6-x)^2=6^2-2\cdot 6\cdot x+x^2=36-12x+x^2;$$
3. $$\left(\frac12 a+b\right)^2=\left(\frac12 a\right)^2+2\cdot \frac12 a\cdot b+b^2=\frac14 a^2+ab+b^2;$$
4. $$(3x-4)^2=(3x)^2-2\cdot 3x\cdot 4+4^2=9x^2-24x+16;$$
5. $$(5m+3n)^2=(5m)^2+2\cdot 5m\cdot 3n+(3n)^2=25m^2+30mn+9n^2;$$
6. $$(0{,}1a+10b)^2=(0{,}1a)^2+2\cdot 0{,}1a\cdot 10b+(10b)^2=0{,}01a^2+2ab+100b^2;$$
7. $$\left(6x-\frac13 y\right)^2=(6x)^2-2\cdot 6x\cdot \frac13 y+\left(\frac13 y\right)^2=36x^2-4xy+\frac19 y^2;$$
8. $$(n^2+1)^2=(n^2)^2+2\cdot n^2\cdot 1+1^2=n^4+2n^2+1;$$
9. $$(x^4-x^2)^2=(x^4)^2-2\cdot x^4\cdot x^2+(x^2)^2=x^8-2x^6+x^4;$$
10. $$(y^4+y^3)^2=(y^4)^2+2\cdot y^4\cdot y^3+(y^3)^2=y^8+2y^7+y^6;$$
11. $$(-3a+4b^3)^2=(-3a)^2+2\cdot (-3a)\cdot 4b^3+(4b^3)^2=9a^2-24ab^3+16b^6;$$
12. $$(-2-5x)^2=(-2)^2+2\cdot (-2)\cdot (-5x)+(-5x)^2=4+20x+25x^2;$$
13. $$\left(1\frac13 m+3\frac35 n\right)^2=\left(\frac43 m\right)^2+2\cdot \frac43 m\cdot \frac{18}{5}n+\left(\frac{18}{5}n\right)^2$$

$$=\frac{16}{9}m^2+\frac{48}{5}mn+\frac{324}{25}n^2;$$

14. $$(6ab^2-a^2b)^2=(6ab^2)^2-2\cdot 6ab^2\cdot a^2b+(a^2b)^2=36a^2b^4-12a^3b^3+a^4b^2;$$
15. $$(5a^4-2a^2b^4)^2=(5a^4)^2-2\cdot 5a^4\cdot 2a^2b^4+(2a^2b^4)^2=25a^8-20a^6b^4+4a^4b^8.$$