Упр.344 ГДЗ Муравин 7 класс (Алгебра)

1) (х^2 — 4х)(х + 1); 6) (5b^3 — 7b^2)(b — 2);
2) (8x^3 — 3x^2)(2x — 3); 7) (1/6 b^4 — 4b)(b — 1/3);
3) (7y^2 + 6y)(5y — 12); 8) (n^2 — 2/3)(n — 0,3);
4) (-0,63p — 0,37p)(10p + 7); 9) (a^2 — 2a + 3)(a — 4);
5) (3a^3 + 4a)(a — 5); 10) (a^2 — 7a — 1)(a + 6).

1. $$\begin{aligned} (x^2-4x)(x+1)&=x^2\cdot x+x^2\cdot 1-4x\cdot x-4x\cdot 1\\ &=x^3+x^2-4x^2-4x\\ &=x^3-3x^2-4x. \end{aligned}$$
2. $$\begin{aligned} (8x^3-3x^2)(2x-3)&=8x^3\cdot 2x+8x^3\cdot(-3)-3x^2\cdot 2x-3x^2\cdot(-3)\\ &=16x^4-24x^3-6x^3+9x^2\\ &=16x^4-30x^3+9x^2. \end{aligned}$$
3. $$\begin{aligned} (7y^2+6y)(5y-12)&=7y^2\cdot 5y+7y^2\cdot(-12)+6y\cdot 5y+6y\cdot(-12)\\ &=35y^3-84y^2+30y^2-72y\\ &=35y^3-54y^2-72y. \end{aligned}$$
4. $$\begin{aligned} (-0{,}63p-0{,}37p)(10p+7)&=(-p)(10p+7)\\ &=-10p^2-7p. \end{aligned}$$
5. $$\begin{aligned} (3a^3+4a)(a-5)&=3a^3\cdot a+3a^3\cdot(-5)+4a\cdot a+4a\cdot(-5)\\ &=3a^4-15a^3+4a^2-20a. \end{aligned}$$
6. $$\begin{aligned} (5b^3-7b^2)(b-2)&=5b^3\cdot b+5b^3\cdot(-2)-7b^2\cdot b-7b^2\cdot(-2)\\ &=5b^4-10b^3-7b^3+14b^2\\ &=5b^4-17b^3+14b^2. \end{aligned}$$
7. $$\begin{aligned} \left(\frac16 b^4-4b\right)\left(b-\frac13\right)&=\frac16 b^4\cdot b+\frac16 b^4\cdot\left(-\frac13\right)-4b\cdot b-4b\cdot\left(-\frac13\right)\\ &=\frac16 b^5-\frac1{18}b^4-4b^2+\frac43 b. \end{aligned}$$
8. $$\begin{aligned} \left(n^2-\frac23\right)(n-0{,}3)&=n^2\cdot n+n^2\cdot(-0{,}3)-\frac23\cdot n-\frac23\cdot(-0{,}3)\\ &=n^3-0{,}3n^2-\frac23 n+0{,}2. \end{aligned}$$
9. $$\begin{aligned} (a^2-2a+3)(a-4)&=a^2\cdot a+a^2\cdot(-4)-2a\cdot a-2a\cdot(-4)+3\cdot a+3\cdot(-4)\\ &=a^3-4a^2-2a^2+8a+3a-12\\ &=a^3-6a^2+11a-12. \end{aligned}$$
10. $$\begin{aligned} (a^2-7a-1)(a+6)&=a^2\cdot a+a^2\cdot 6-7a\cdot a-7a\cdot 6-1\cdot a-1\cdot 6\\ &=a^3+6a^2-7a^2-42a-a-6\\ &=a^3-a^2-43a-6. \end{aligned}$$

Ответ

1) $$x^3-3x^2-4x$$; 2) $$16x^4-30x^3+9x^2$$; 3) $$35y^3-54y^2-72y$$; 4) $$-10p^2-7p$$; 5) $$3a^4-15a^3+4a^2-20a$$; 6) $$5b^4-17b^3+14b^2$$; 7) $$\frac16 b^5-\frac1{18}b^4-4b^2+\frac43 b$$; 8) $$n^3-0{,}3n^2-\frac23 n+0{,}2$$; 9) $$a^3-6a^2+11a-12$$; 10) $$a^3-a^2-43a-6$$.