Упр.92 Вариант 2 Дидактические материалы ГДЗ Мерзляк Полонский 7 класс (Алгебра)

1) 2х(х^2 + 8x — 3);
2) -3a(a^2 + 2ab — 5b);
3) (4y^2 — 2y^3 + 16) · (-2,5y);
4) 0,3mn(2mn^2 — 4m^2 n + 3mn);
5) 1 3/4 a^2 b(4b^2 — 8/7 ab + 16/21 a^3);
6) -7x^2 y^3 (5x^4 — xy — 3y^3).

1. $$2x(x^2+8x-3)=2x\cdot x^2+2x\cdot 8x-2x\cdot 3=2x^3+16x^2-6x.$$
2. $$-3a(a^2+2ab-5b)=-3a\cdot a^2-3a\cdot 2ab+(-3a)\cdot(-5b)=-3a^3-6a^2b+15ab.$$
3. $$\begin{aligned}
   (4y^2-2y^3+16)\cdot(-2{,}5y)&=-2{,}5y\cdot 4y^2+(-2{,}5y)\cdot(-2y^3)+(-2{,}5y)\cdot 16\\
   &=-10y^3+5y^4-40y.
   \end{aligned}$$
4. $$\begin{aligned}
   0{,}3mn(2mn^2-4m^2n+3mn)&=0{,}3mn\cdot 2mn^2-0{,}3mn\cdot 4m^2n+0{,}3mn\cdot 3mn\\
   &=0{,}6m^2n^3-1{,}2m^3n^2+0{,}9m^2n^2.
   \end{aligned}$$
5. $$\begin{aligned}
   1\frac{3}{4}a^2b\left(4b^2-\frac{8}{7}ab+\frac{16}{21}a^3\right)
   &=\frac{7}{4}a^2b\cdot 4b^2-\frac{7}{4}a^2b\cdot \frac{8}{7}ab+\frac{7}{4}a^2b\cdot \frac{16}{21}a^3\\
   &=7a^2b^3-2a^3b^2+\frac{4}{3}a^5b.
   \end{aligned}$$
6. $$\begin{aligned}
   -7x^2y^3(5x^4-xy-3y^3)
   &=-7x^2y^3\cdot 5x^4-7x^2y^3\cdot(-xy)-7x^2y^3\cdot(-3y^3)\\
   &=-35x^6y^3+7x^3y^4+21x^2y^6.
   \end{aligned}$$

Ответ

1) $$2x^3+16x^2-6x$$
2) $$-3a^3-6a^2b+15ab$$
3) $$5y^4-10y^3-40y$$
4) $$0{,}6m^2n^3-1{,}2m^3n^2+0{,}9m^2n^2$$
5) $$7a^2b^3-2a^3b^2+\frac{4}{3}a^5b$$
6) $$-35x^6y^3+7x^3y^4+21x^2y^6$$