Упр.698 ГДЗ Мерзляк Полонский 7 класс (Алгебра)

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

Из условия $$x^3-y^2=2$$ получаем:

$$\begin{aligned} x^9-6x^3y^2-y^6&=(x^9-y^6)-6x^3y^2\\ &=(x^3-y^2)(x^6+x^3y^2+y^4)-6x^3y^2\\ &=2(x^6+x^3y^2+y^4)-6x^3y^2\\ &=2x^6-4x^3y^2+2y^4\\ &=2(x^3-y^2)^2\\ &=2\cdot 2^2=8 \end{aligned}$$

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) $$-10x+74$$;
$$x^9-6x^3y^2-y^6=8$$