Упр.12.9 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) (x+2)(x-1)(x-4);
2) (2x+1)(x+5)(x-6);
3) (x^2-2x+3)(x^2+2x-3);
4) (a+2b-c)(a-3b+2c);
5) (a+b)(a^3-a^2 b+ab^2-b^3 );
6) (x-1)(x^4+x^3+x^2+x+1).

1. $$\begin{aligned} (x+2)(x-1)(x-4) &= (x+2)(x^2-5x+4) \\ &= x^3-5x^2+4x+2x^2-10x+8 \\ &= x^3-3x^2-6x+8. \end{aligned}$$

2. $$\begin{aligned} (2x+1)(x+5)(x-6) &= (2x+1)(x^2-x-30) \\ &= 2x^3-2x^2-60x+x^2-x-30 \\ &= 2x^3-x^2-61x-30. \end{aligned}$$

3. $$\begin{aligned} (x^2-2x+3)(x^2+2x-3) &= x^4+2x^3-3x^2-2x^3-4x^2+6x+3x^2+6x-9 \\ &= x^4-4x^2+12x-9. \end{aligned}$$

4. $$\begin{aligned} (a+2b-c)(a-3b+2c) &= a^2-3ab+2ac+2ab-6b^2+4bc-ac+3bc-2c^2 \\ &= a^2-ab+ac-6b^2+7bc-2c^2. \end{aligned}$$

5. $$\begin{aligned} (a+b)(a^3-a^2b+ab^2-b^3) &= a^4-a^3b+a^2b^2-ab^3+a^3b-a^2b^2+ab^3-b^4 \\ &= a^4-b^4. \end{aligned}$$

6. $$\begin{aligned} (x-1)(x^4+x^3+x^2+x+1) &= x^5+x^4+x^3+x^2+x-x^4-x^3-x^2-x-1 \\ &= x^5-1. \end{aligned}$$

Ответ

1) $$x^3-3x^2-6x+8$$; 2) $$2x^3-x^2-61x-30$$; 3) $$x^4-4x^2+12x-9$$; 4) $$a^2-ab+ac-6b^2+7bc-2c^2$$; 5) $$a^4-b^4$$; 6) $$x^5-1$$.