Упр.12.1 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1. 12.1. Выполните умножение: 1) $$(a-2)(b+5)$$; 7) $$(-2m-3)(5-m)$$; 2) $$(m+n)(p-k)$$; 8) $$(5x^2-x)(6x^2+4x)$$; 3) $$(x-8)(x+4)$$; 9) $$(-c-4)(c^3+3)$$; 4) $$(x-10)(x-9)$$; 10) $$(x-5)(x^2+4x-3)$$; 5) $$(c+5)(c+8)$$; 11) $$(2a+3)(4a^2-4a+3)$$; 6) $$(3y+1)(4y-6)$$; 12) $$a(5a-4)(3a-2)$$.

1. $$\begin{aligned} (a-2)(b+5) &= ab+5a-2b-10 \end{aligned}$$
2. $$\begin{aligned} (m+n)(p-k) &= mp-mk+np-nk \end{aligned}$$
3. $$\begin{aligned} (x-8)(x+4) &= x^2+4x-8x-32 \\ &= x^2-4x-32 \end{aligned}$$
4. $$\begin{aligned} (x-10)(x-9) &= x^2-9x-10x+90 \\ &= x^2-19x+90 \end{aligned}$$
5. $$\begin{aligned} (c+5)(c+8) &= c^2+8c+5c+40 \\ &= c^2+13c+40 \end{aligned}$$
6. $$\begin{aligned} (3y+1)(4y-6) &= 12y^2-18y+4y-6 \\ &= 12y^2-14y-6 \end{aligned}$$
7. $$\begin{aligned} (-2m-3)(5-m) &= -10m+2m^2-15+3m \\ &= 2m^2-7m-15 \end{aligned}$$
8. $$\begin{aligned} (5x^2-x)(6x^2+4x) &= 30x^4+20x^3-6x^3-4x^2 \\ &= 30x^4+14x^3-4x^2 \end{aligned}$$
9. $$\begin{aligned} (-c-4)(c^3+3) &= -c^4-3c-4c^3-12 \\ &= -c^4-4c^3-3c-12 \end{aligned}$$
10. $$\begin{aligned} (x-5)(x^2+4x-3) &= x^3+4x^2-3x-5x^2-20x+15 \\ &= x^3-x^2-23x+15 \end{aligned}$$
11. $$\begin{aligned} (2a+3)(4a^2-4a+3) &= 8a^3-8a^2+6a+12a^2-12a+9 \\ &= 8a^3+4a^2-6a+9 \end{aligned}$$
12. $$\begin{aligned} a(5a-4)(3a-2) &= a(15a^2-10a-12a+8) \\ &= a(15a^2-22a+8) \\ &= 15a^3-22a^2+8a \end{aligned}$$

Ответ

1. $$ab+5a-2b-10$$
2. $$mp-mk+np-nk$$
3. $$x^2-4x-32$$
4. $$x^2-19x+90$$
5. $$c^2+13c+40$$
6. $$12y^2-14y-6$$
7. $$2m^2-7m-15$$
8. $$30x^4+14x^3-4x^2$$
9. $$-c^4-4c^3-3c-12$$
10. $$x^3-x^2-23x+15$$
11. $$8a^3+4a^2-6a+9$$
12. $$15a^3-22a^2+8a$$