Упр.35.38 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

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

1. $$\begin{aligned} (a+5)(a-2)+(a+4)(a-5) &= a^2-2a+5a-10+a^2-5a+4a-20 \\ &= 2a^2+2a-30. \end{aligned}$$
2. $$\begin{aligned} (y-8)(2y+1)-(3y+1)(y-6) &= 2y^2+y-16y-8-(3y^2-18y+y-6) \\ &= 2y^2-15y-8-3y^2+17y+6 \\ &= -y^2+2y-2. \end{aligned}$$
3. $$\begin{aligned} (2x-3y)(2x+3y)+(3x+2y)(3x-2y) &= 4x^2-9y^2+9x^2-4y^2 \\ &= 13x^2-13y^2. \end{aligned}$$
4. $$\begin{aligned} (x+1)^2-(x-3)(x+3) &= x^2+2x+1-(x^2-9) \\ &= 2x+10. \end{aligned}$$
5. $$\begin{aligned} (y-4)(y+3)-(y-6)^2 &= y^2+3y-4y-12-(y^2-12y+36) \\ &= y^2-y-12-y^2+12y-36 \\ &= 11y-48. \end{aligned}$$

Ответ

1) $$2a^2+2a-30$$; 2) $$-y^2+2y-2$$; 3) $$13x^2-13y^2$$; 4) $$2x+10$$; 5) $$11y-48$$.