Упр.17.6 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) (x-12)^2+24x; 2) (x+8)^2-x(x+5);
3) 2x(x+2)-(x-2)^2; 4) (y+7)^2+(y+2)(y-7);
5) (a+1)(a-1)-(a+4)^2; 6) (x-10)(9-x)+(x+10)^2.

1. $$\begin{aligned} (x-12)^2+24x&=x^2-24x+144+24x\\ &=x^2+144 \end{aligned}$$
2. $$\begin{aligned} (x+8)^2-x(x+5)&=x^2+16x+64-x^2-5x\\ &=11x+64 \end{aligned}$$
3. $$\begin{aligned} 2x(x+2)-(x-2)^2&=2x^2+4x-(x^2-4x+4)\\ &=2x^2+4x-x^2+4x-4\\ &=x^2+8x-4 \end{aligned}$$
4. $$\begin{aligned} (y+7)^2+(y+2)(y-7)&=y^2+14y+49+y^2-7y+2y-14\\ &=2y^2+9y+35 \end{aligned}$$
5. $$\begin{aligned} (a+1)(a-1)-(a+4)^2&=a^2-1-(a^2+8a+16)\\ &=a^2-1-a^2-8a-16\\ &=-8a-17 \end{aligned}$$
6. $$\begin{aligned} (x-10)(9-x)+(x+10)^2&=9x-x^2-90+10x+x^2+20x+100\\ &=39x+10 \end{aligned}$$

Ответ

1) $$x^2+144$$; 2) $$11x+64$$; 3) $$x^2+8x-4$$; 4) $$2y^2+9y+35$$; 5) $$-8a-17$$; 6) $$39x+10$$.