Упр.35.30 Часть 2 ГДЗ Мордкович Семенов 7 класс (Алгебра)

а) а^3 b^3 — 1; г) 64х^6 y^3 — 27;
б) 27n^3 — 8m^6; д) 125m^9 — 27n^6;
в) 125а^3 b^6 + 216b^3; е) 27m^9 n^3 + 64m^3.

Используем формулы суммы и разности кубов:

$$a^3-b^3=(a-b)(a^2+ab+b^2),$$

$$a^3+b^3=(a+b)(a^2-ab+b^2).$$

1. $$a^3b^3-1=(ab)^3-1^3=(ab-1)(a^2b^2+ab+1).$$

2. $$27n^3-8m^6=(3n)^3-(2m^2)^3=(3n-2m^2)(9n^2+6m^2n+4m^4).$$

3. $$125a^3b^6+216b^3=(5ab^2)^3+(6b)^3=(5ab^2+6b)(25a^2b^4-30ab^3+36b^2).$$

4. $$64x^6y^3-27=(4x^2y)^3-3^3=(4x^2y-3)(16x^4y^2+12x^2y+9).$$

5. $$125m^9-27n^6=(5m^3)^3-(3n^2)^3=(5m^3-3n^2)(25m^6+15m^3n^2+9n^4).$$

6. $$27m^9n^3+64m^3=(3m^3n)^3+(4m)^3=(3m^3n+4m)(9m^6n^2-12m^4n+16m^2).$$

Ответ

а) $$\left(ab-1\right)\left(a^2b^2+ab+1\right);$$
б) $$\left(3n-2m^2\right)\left(9n^2+6m^2n+4m^4\right);$$
в) $$\left(5ab^2+6b\right)\left(25a^2b^4-30ab^3+36b^2\right);$$
г) $$\left(4x^2y-3\right)\left(16x^4y^2+12x^2y+9\right);$$
д) $$\left(5m^3-3n^2\right)\left(25m^6+15m^3n^2+9n^4\right);$$
е) $$\left(3m^3n+4m\right)\left(9m^6n^2-12m^4n+16m^2\right).$$