Упр.529 ГДЗ Колягин Ткачёва 9 класс (Алгебра)

1) (x-6)(5+x)-x^2(x^2-5x+1);
2) (x+7)(5-x)-x^2(x^3+2x-1);
3) (b-3a)^2+8(a-1/2 b)(a+1/2 b);
4) (3a+6)^2+4(b-1/2 a)(b+1/2 a).

1. $$\begin{aligned} (x-6)(5+x)-x^2(x^2-5x+1) &= (x-6)(x+5)-x^4+5x^3-x^2 \\ &= x^2+5x-6x-30-x^4+5x^3-x^2 \\ &= -x^4+5x^3-x-30. \end{aligned}$$
2. $$\begin{aligned} (x+7)(5-x)-x^2(x^3+2x-1) &= 5x-x^2+35-7x-x^5-2x^3+x^2 \\ &= 35-2x-2x^3-x^5. \end{aligned}$$
3. $$\begin{aligned} (b-3a)^2+8\left(a-\frac12 b\right)\left(a+\frac12 b\right) &= (b-3a)^2+8\left(a^2-\frac14 b^2\right) \\ &= b^2-6ab+9a^2+8a^2-2b^2 \\ &= 17a^2-b^2-6ab. \end{aligned}$$
4. $$\begin{aligned} (3a+6)^2+4\left(b-\frac12 a\right)\left(b+\frac12 a\right) &= (3a+6)^2+4\left(b^2-\frac14 a^2\right) \\ &= 9a^2+36a+36+4b^2-a^2 \\ &= 8a^2+4b^2+36a+36. \end{aligned}$$

Ответ

1) $$-x^4+5x^3-x-30$$; 2) $$-x^5-2x^3-2x+35$$; 3) $$17a^2-b^2-6ab$$; 4) $$8a^2+4b^2+36a+36$$.