Упр.23 ГДЗ Мерзляк Полонский 8 класс (Алгебра)

1) х2 — 9;
2) 25 — 4у2;
3) 36m2 — 49n2;
4) а2b2 — 81;
5) 100m6 — 1;
6) а10 — b6;
7) с3 — d3;
8) а3 + 8;
9) 27m6 — n9.

1. $$x^2-9=x^2-3^2=(x-3)(x+3).$$
2. $$25-4y^2=5^2-(2y)^2=(5-2y)(5+2y).$$
3. $$36m^2-49n^2=(6m)^2-(7n)^2=(6m-7n)(6m+7n).$$
4. $$a^2b^2-81=(ab)^2-9^2=(ab-9)(ab+9).$$
5. $$100m^6-1=(10m^3)^2-1^2=(10m^3-1)(10m^3+1).$$
6. $$a^{10}-b^6=(a^5)^2-(b^3)^2=(a^5-b^3)(a^5+b^3).$$
7. $$c^3-d^3=(c-d)(c^2+cd+d^2).$$
8. $$a^3+8=a^3+2^3=(a+2)(a^2-2a+4).$$
9. $$27m^6-n^9=(3m^2)^3-(n^3)^3=(3m^2-n^3)(9m^4+3m^2n^3+n^6).$$

Ответ

$$x^2-9=(x-3)(x+3),$$
$$25-4y^2=(5-2y)(5+2y),$$
$$36m^2-49n^2=(6m-7n)(6m+7n),$$
$$a^2b^2-81=(ab-9)(ab+9),$$
$$100m^6-1=(10m^3-1)(10m^3+1),$$
$$a^{10}-b^6=(a^5-b^3)(a^5+b^3),$$
$$c^3-d^3=(c-d)(c^2+cd+d^2),$$
$$a^3+8=(a+2)(a^2-2a+4),$$
$$27m^6-n^9=(3m^2-n^3)(9m^4+3m^2n^3+n^6).$$