Упр.26.27 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) (c+2)(c-3)-(c+1)(c+3);
2) (p+4)(p-11)+(p+6)^2;
3) 3(x-5)^2-(8x^2-10x);
4) 7(2y-5)^2-2(7y-1)^2.

1. $$\begin{aligned} (c+2)(c-3)-(c+1)(c+3) &= c^2-3c+2c-6-(c^2+3c+c+3) \\ &= c^2-c-6-c^2-4c-3 \\ &= -5c-9. \end{aligned}$$

2. $$\begin{aligned} (p+4)(p-11)+(p+6)^2 &= p^2-11p+4p-44+p^2+12p+36 \\ &= 2p^2+5p-8. \end{aligned}$$

3. $$\begin{aligned} 3(x-5)^2-(8x^2-10x) &= 3(x^2-10x+25)-8x^2+10x \\ &= 3x^2-30x+75-8x^2+10x \\ &= -5x^2-20x+75. \end{aligned}$$

4. $$\begin{aligned} 7(2y-5)^2-2(7y-1)^2 &= 7(4y^2-20y+25)-2(49y^2-14y+1) \\ &= 28y^2-140y+175-98y^2+28y-2 \\ &= -70y^2-112y+173. \end{aligned}$$

Ответ

1) $$-5c-9$$; 2) $$2p^2+5p-8$$; 3) $$-5x^2-20x+75$$; 4) $$-70y^2-112y+173$$.