Упр.17.5 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) a^2+(3a-b)^2; 2) (4x+5)^2-40x;
3) 50a^2-(7a-1)^2; 4) c^2+36-(c-6)^2;
5) (x-2)^2+x(x+10); 6) 3m(m-4)-(m+2)^2;
7) (y-9)^2+(4-y)(y+6); 8) (x-4)(x+4)-(x-1)^2;
9) (2a-3b)^2+(3a+2b)^2; 10) (x-5)^2-(x-7)(x+7).

1. $$a^2+(3a-b)^2=a^2+9a^2-6ab+b^2=10a^2-6ab+b^2.$$
2. $$\begin{aligned} (4x+5)^2-40x&=16x^2+40x+25-40x\\ &=16x^2+25. \end{aligned}$$
3. $$\begin{aligned} 50a^2-(7a-1)^2&=50a^2-(49a^2-14a+1)\\ &=50a^2-49a^2+14a-1\\ &=a^2+14a-1. \end{aligned}$$
4. $$\begin{aligned} c^2+36-(c-6)^2&=c^2+36-(c^2-12c+36)\\ &=c^2+36-c^2+12c-36\\ &=12c. \end{aligned}$$
5. $$\begin{aligned} (x-2)^2+x(x+10)&=x^2-4x+4+x^2+10x\\ &=2x^2+6x+4. \end{aligned}$$
6. $$\begin{aligned} 3m(m-4)-(m+2)^2&=3m^2-12m-(m^2+4m+4)\\ &=3m^2-12m-m^2-4m-4\\ &=2m^2-16m-4. \end{aligned}$$
7. $$\begin{aligned} (y-9)^2+(4-y)(y+6)&=y^2-18y+81+4y+24-y^2-6y\\ &=-20y+105. \end{aligned}$$
8. $$\begin{aligned} (x-4)(x+4)-(x-1)^2&=x^2-16-(x^2-2x+1)\\ &=x^2-16-x^2+2x-1\\ &=2x-17. \end{aligned}$$
9. $$\begin{aligned} (2a-3b)^2+(3a+2b)^2&=4a^2-12ab+9b^2+9a^2+12ab+4b^2\\ &=13a^2+13b^2. \end{aligned}$$
10. $$\begin{aligned} (x-5)^2-(x-7)(x+7)&=x^2-10x+25-(x^2-49)\\ &=x^2-10x+25-x^2+49\\ &=-10x+74. \end{aligned}$$

Ответ

1) $$10a^2-6ab+b^2$$; 2) $$16x^2+25$$; 3) $$a^2+14a-1$$; 4) $$12c$$; 5) $$2x^2+6x+4$$; 6) $$2m^2-16m-4$$; 7) $$-20y+105$$; 8) $$2x-17$$; 9) $$13a^2+13b^2$$; 10) $$-10x+74$$.