Упр.400 ГДЗ Мерзляк Полонский 7 класс (Алгебра)

1. $$\begin{aligned} (2a+b)-(b-2a)&=2a+b-b+2a\\ &=4a; \end{aligned}$$

2. $$\begin{aligned} (3a-4)+(3-5a)&=3a-4+3-5a\\ &=-2a-1; \end{aligned}$$

3. $$\begin{aligned} (m+n)-(2m+n)-(m-4n)&=m+n-2m-n-m+4n\\ &=-2m+4n; \end{aligned}$$

4. $$\begin{aligned} (5c-2)-(6c+1)+(c-8)&=5c-2-6c-1+c-8\\ &=-11; \end{aligned}$$

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

6. $$\begin{aligned} (2x+1)(x+5)(x-6)&=(2x^2+11x+5)(x-6)\\ &=2x^3-12x^2+11x^2-66x+5x-30\\ &=2x^3-x^2-61x-30; \end{aligned}$$

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

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

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

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

Ответ

1) $$4a$$; 2) $$-2a-1$$; 3) $$-2m+4n$$; 4) $$-11$$; 5) $$x^3-3x^2-6x+8$$; 6) $$2x^3-x^2-61x-30$$; 7) $$x^4-4x^2+12x-9$$; 8) $$a^2-ab+ac-6b^2+7bc-2c^2$$; 9) $$a^4-b^4$$; 10) $$x^5-1$$.