Упр.12.2 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) (a+b)(c-d); 6) (3y-5)(2y-12);
2) (x-6)(x-4); 7) (2x^2-3)(x^2+4);
3) (a-3)(a+7); 8) (x-6)(x^2-2x+9);
4) (11-c)(c+8); 9) (5x-y)(2x^2+xy-3y^2 );
5) (d+13)(2d-1); 10) b(6b+7)(3b-4).

1. $$\begin{aligned} (a+b)(c-d)&=ac-ad+bc-bd \end{aligned}$$
2. $$\begin{aligned} (x-6)(x-4)&=x^2-4x-6x+24\\ &=x^2-10x+24 \end{aligned}$$
3. $$\begin{aligned} (a-3)(a+7)&=a^2+7a-3a-21\\ &=a^2+4a-21 \end{aligned}$$
4. $$\begin{aligned} (11-c)(c+8)&=11c+88-c^2-8c\\ &=-c^2+3c+88 \end{aligned}$$
5. $$\begin{aligned} (d+13)(2d-1)&=2d^2-d+26d-13\\ &=2d^2+25d-13 \end{aligned}$$
6. $$\begin{aligned} (3y-5)(2y-12)&=6y^2-36y-10y+60\\ &=6y^2-46y+60 \end{aligned}$$
7. $$\begin{aligned} (2x^2-3)(x^2+4)&=2x^4+8x^2-3x^2-12\\ &=2x^4+5x^2-12 \end{aligned}$$
8. $$\begin{aligned} (x-6)(x^2-2x+9)&=x^3-2x^2+9x-6x^2+12x-54\\ &=x^3-8x^2+21x-54 \end{aligned}$$
9. $$\begin{aligned} (5x-y)(2x^2+xy-3y^2)&=10x^3+5x^2y-15xy^2-2x^2y-xy^2+3y^3\\ &=10x^3+3x^2y-16xy^2+3y^3 \end{aligned}$$
10. $$\begin{aligned} b(6b+7)(3b-4)&=(6b^2+7b)(3b-4)\\ &=18b^3-24b^2+21b^2-28b\\ &=18b^3-3b^2-28b \end{aligned}$$

Ответ

1) $$ac-ad+bc-bd$$;
2) $$x^2-10x+24$$;
3) $$a^2+4a-21$$;
4) $$-c^2+3c+88$$;
5) $$2d^2+25d-13$$;
6) $$6y^2-46y+60$$;
7) $$2x^4+5x^2-12$$;
8) $$x^3-8x^2+21x-54$$;
9) $$10x^3+3x^2y-16xy^2+3y^3$$;
10) $$18b^3-3b^2-28b$$.