Упр.12.4 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) (a-2)(a-1)-a(a+1);
2) (b-5)(b+10)+(b+6)(b-8);
3) (2c+3)(3c+2)-(2c+7)(2c-7);
4) (3d+5)(5d-1)-(6d-3)(2-8d).

1. $$\begin{aligned} (a-2)(a-1)-a(a+1) &= a^2-a-2a+2-a^2-a \\ &= -4a+2. \end{aligned}$$

2. $$\begin{aligned} (b-5)(b+10)+(b+6)(b-8) &= b^2+10b-5b-50+b^2-8b+6b-48 \\ &= 2b^2+3b-98. \end{aligned}$$

3. $$\begin{aligned} (2c+3)(3c+2)-(2c+7)(2c-7) &= 6c^2+4c+9c+6-(4c^2-49) \\ &= 6c^2+13c+6-4c^2+49 \\ &= 2c^2+13c+55. \end{aligned}$$

4. $$\begin{aligned} (3d+5)(5d-1)-(6d-3)(2-8d) &= 15d^2-3d+25d-5-(12d-48d^2-6+24d) \\ &= 15d^2+22d-5+48d^2-36d+6 \\ &= 63d^2-14d+1. \end{aligned}$$

Ответ

1) $$-4a+2$$; 2) $$2b^2+3b-98$$; 3) $$2c^2+13c+55$$; 4) $$63d^2-14d+1$$.