Упр.123 Вариант 1 Дидактические материалы ГДЗ Мерзляк Полонский 7 класс (Алгебра)

1) x^2 — 4;
2) 25 — 9a^2;
3) 36m^2 — 100n^2;
4) 0,04p^2 — 1,69q^2;
5) x^2 y^2 — 4/9;
6) a^4 — b^6;
7) 0,01c^2 — d^8;
8) 0,81y^10 — 400z^12;
9) -1 + 49a^4 b^8;
10) 1 7/9 m^2 n^2 — 1 11/25 a^6 b^2.

1. $$x^2-4=x^2-2^2=(x-2)(x+2)$$
2. $$25-9a^2=5^2-(3a)^2=(5-3a)(5+3a)$$
3. $$36m^2-100n^2=(6m)^2-(10n)^2=(6m-10n)(6m+10n)$$
4. $$0{,}04p^2-1{,}69q^2=(0{,}2p)^2-(1{,}3q)^2=(0{,}2p-1{,}3q)(0{,}2p+1{,}3q)$$
5. $$x^2y^2-\frac{4}{9}=(xy)^2-\left(\frac{2}{3}\right)^2=\left(xy-\frac{2}{3}\right)\left(xy+\frac{2}{3}\right)$$
6. $$a^4-b^6=(a^2)^2-(b^3)^2=(a^2-b^3)(a^2+b^3)$$
7. $$0{,}01c^2-d^8=(0{,}1c)^2-(d^4)^2=(0{,}1c-d^4)(0{,}1c+d^4)$$
8. $$0{,}81y^{10}-400z^{12}=(0{,}9y^5)^2-(20z^6)^2=(0{,}9y^5-20z^6)(0{,}9y^5+20z^6)$$
9. $$-1+49a^4b^8=49a^4b^8-1=(7a^2b^4)^2-1^2=(7a^2b^4-1)(7a^2b^4+1)$$
10. $$1\frac{7}{9}m^2n^2-1\frac{11}{25}a^6b^2=\frac{16}{9}m^2n^2-\frac{36}{25}a^6b^2$$
    $$=\left(\frac{4}{3}mn\right)^2-\left(\frac{6}{5}a^3b\right)^2=\left(\frac{4}{3}mn-\frac{6}{5}a^3b\right)\left(\frac{4}{3}mn+\frac{6}{5}a^3b\right)$$

Ответ

1) $$\left(x-2\right)\left(x+2\right)$$;
2) $$\left(5-3a\right)\left(5+3a\right)$$;
3) $$\left(6m-10n\right)\left(6m+10n\right)$$;
4) $$\left(0{,}2p-1{,}3q\right)\left(0{,}2p+1{,}3q\right)$$;
5) $$\left(xy-\frac{2}{3}\right)\left(xy+\frac{2}{3}\right)$$;
6) $$\left(a^2-b^3\right)\left(a^2+b^3\right)$$;
7) $$\left(0{,}1c-d^4\right)\left(0{,}1c+d^4\right)$$;
8) $$\left(0{,}9y^5-20z^6\right)\left(0{,}9y^5+20z^6\right)$$;
9) $$\left(7a^2b^4-1\right)\left(7a^2b^4+1\right)$$;
10) $$\left(\frac{4}{3}mn-\frac{6}{5}a^3b\right)\left(\frac{4}{3}mn+\frac{6}{5}a^3b\right)$$.