Упр.15.7 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) (9a-2)(9a+2)-18a^2;
2) 25m^2-(5m-7)(5m+7);
3) (b+7)(b-4)+(2b-6)(2b+6);
4) 4x(3x-10y)-(4x+y)(4x-y).

1. $$\begin{aligned} (9a-2)(9a+2)-18a^2 &= (9a)^2-2^2-18a^2 \\ &= 81a^2-4-18a^2 \\ &= 63a^2-4. \end{aligned}$$

2. $$\begin{aligned} 25m^2-(5m-7)(5m+7) &= 25m^2-(25m^2-49) \\ &= 25m^2-25m^2+49 \\ &= 49. \end{aligned}$$

3. $$\begin{aligned} (b+7)(b-4)+(2b-6)(2b+6) &= b^2-4b+7b-28+4b^2-36 \\ &= 5b^2+3b-64. \end{aligned}$$

4. $$\begin{aligned} 4x(3x-10y)-(4x+y)(4x-y) &= 12x^2-40xy-(16x^2-y^2) \\ &= 12x^2-40xy-16x^2+y^2 \\ &= y^2-40xy-4x^2. \end{aligned}$$

Ответ

1) $$63a^2-4$$; 2) $$49$$; 3) $$5b^2+3b-64$$; 4) $$y^2-40xy-4x^2$$.