Упр.2 Вариант 1 Дидактические материалы ГДЗ Мерзляк Полонский 8 класс (Алгебра)

1) (x-2)(x-11)-2x(4-3x);
2) (a+6)(a-3)+(a-4)(a+5);
3) (y-8)(2y-1)-(3y+1)(5y-2);
4) (x+2)^2-(x-3)(x+3);
5) (7a-5b)(7a+5b)-(4a+7b)^2;
6) (y-2)(y+3)-(y-1)^2+(5-y)(y+5).

1. $$\begin{aligned} (x-2)(x-11)-2x(4-3x) &= x^2-11x-2x+22-8x+6x^2 \\ &= 7x^2-21x+22. \end{aligned}$$

2. $$\begin{aligned} (a+6)(a-3)+(a-4)(a+5) &= a^2-3a+6a-18+a^2+5a-4a-20 \\ &= 2a^2+4a-38. \end{aligned}$$

3. $$\begin{aligned} (y-8)(2y-1)-(3y+1)(5y-2) &= 2y^2-y-16y+8-15y^2+6y-5y+2 \\ &= -13y^2-16y+10. \end{aligned}$$

4. $$\begin{aligned} (x+2)^2-(x-3)(x+3) &= x^2+4x+4-(x^2-9) \\ &= 4x+13. \end{aligned}$$

5. $$\begin{aligned} (7a-5b)(7a+5b)-(4a+7b)^2 &= 49a^2-25b^2-(16a^2+56ab+49b^2) \\ &= 33a^2-56ab-74b^2. \end{aligned}$$

6. $$\begin{aligned} (y-2)(y+3)-(y-1)^2+(5-y)(y+5) &= y^2+y-6-(y^2-2y+1)+25-y^2 \\ &= -y^2+3y+18. \end{aligned}$$

Ответ

1) $$7x^2-21x+22$$; 2) $$2a^2+4a-38$$; 3) $$-13y^2-16y+10$$; 4) $$4x+13$$; 5) $$33a^2-56ab-74b^2$$; 6) $$-y^2+3y+18$$.