Упр.381 ГДЗ Муравин 7 класс (Алгебра)

1) (x — 3)^2 — x(x + 9);
2) (2а + 5)^2 — 5(4а + 5);
3) (а — 3)(а + 3) + а(а + 4);
4) (4x + 5y)^2 — (4x — 5у)^2;
5) (b + 7с)^2 — (7с — b)^2;
6) (4 — у)(4 + y)(16 + у^2);
7) (р — 3)^2 (р + 3)^2;
8) (10 — с^2)(10 + с^2)(100 + с^4).

1. $$\begin{aligned} (x-3)^2-x(x+9)&=x^2-6x+9-x^2-9x\\ &=-15x+9 \end{aligned}$$
2. $$\begin{aligned} (2a+5)^2-5(4a+5)&=4a^2+20a+25-20a-25\\ &=4a^2 \end{aligned}$$
3. $$\begin{aligned} (a-3)(a+3)+a(a+4)&=a^2-9+a^2+4a\\ &=2a^2+4a-9 \end{aligned}$$
4. $$\begin{aligned} (4x+5y)^2-(4x-5y)^2&=(16x^2+40xy+25y^2)-(16x^2-40xy+25y^2)\\ &=80xy \end{aligned}$$
5. $$\begin{aligned} (b+7c)^2-(7c-b)^2&=(b^2+14bc+49c^2)-(49c^2-14bc+b^2)\\ &=28bc \end{aligned}$$
6. $$\begin{aligned} (4-y)(4+y)(16+y^2)&=(16-y^2)(16+y^2)\\ &=16^2-(y^2)^2\\ &=256-y^4 \end{aligned}$$
7. $$\begin{aligned} (p-3)^2(p+3)^2&=(p^2-9)^2\\ &=p^4-18p^2+81 \end{aligned}$$
8. $$\begin{aligned} (10-c^2)(10+c^2)(100+c^4)&=(100-c^4)(100+c^4)\\ &=100^2-(c^4)^2\\ &=10000-c^8 \end{aligned}$$

Ответ

1) $$-15x+9$$; 2) $$4a^2$$; 3) $$2a^2+4a-9$$; 4) $$80xy$$; 5) $$28bc$$; 6) $$256-y^4$$; 7) $$p^4-18p^2+81$$; 8) $$10000-c^8$$.