Упр.20.3 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) (a+1)^3; 2) (m-3)^3; 3) (a+2b)^3;
4) (3-n)^3; 5) (-2+3x)^3; 6) (-3-2y)^3.

1. $$\begin{aligned} (a+1)^3&=a^3+3a^2\cdot 1+3a\cdot 1^2+1^3\\ &=a^3+3a^2+3a+1. \end{aligned}$$
2. $$\begin{aligned} (m-3)^3&=m^3-3m^2\cdot 3+3m\cdot 3^2-3^3\\ &=m^3-9m^2+27m-27. \end{aligned}$$
3. $$\begin{aligned} (a+2b)^3&=a^3+3a^2\cdot 2b+3a\cdot (2b)^2+(2b)^3\\ &=a^3+6a^2b+12ab^2+8b^3. \end{aligned}$$
4. $$\begin{aligned} (3-n)^3&=3^3-3\cdot 3^2\cdot n+3\cdot 3\cdot n^2-n^3\\ &=27-27n+9n^2-n^3. \end{aligned}$$
5. $$\begin{aligned} (-2+3x)^3&=(-2)^3+3\cdot (-2)^2\cdot 3x+3\cdot (-2)\cdot (3x)^2+(3x)^3\\ &=-8+36x-54x^2+27x^3. \end{aligned}$$
6. $$\begin{aligned} (-3-2y)^3&=(-3)^3+3\cdot (-3)^2\cdot (-2y)+3\cdot (-3)\cdot (-2y)^2+(-2y)^3\\ &=-27-54y-36y^2-8y^3. \end{aligned}$$

Ответ

1) $$a^3+3a^2+3a+1$$; 2) $$m^3-9m^2+27m-27$$; 3) $$a^3+6a^2b+12ab^2+8b^3$$; 4) $$27-27n+9n^2-n^3$$; 5) $$27x^3-54x^2+36x-8$$; 6) $$-8y^3-36y^2-54y-27$$.