Упр.123 Вариант 2 Дидактические материалы ГДЗ Мерзляк Полонский 7 класс (Алгебра)

1) x^2-25;
2) 36-16y^2;
3) 4x^2-81y^2;
4) 0,09t^2-121p^2;
5) a^2 b^2-16/9;
6) a^8-x^10;
7) 0,04b^4-a^12;
8) 1,69y^14-900z^8;
9)-1+36a^6 b^4);
10) 1 24/25 m^6 n^4-1 9/16 a^2 b^8.

1. $$x^2-25=x^2-5^2=(x-5)(x+5)$$
2. $$36-16y^2=6^2-(4y)^2=(6-4y)(6+4y)$$
3. $$4x^2-81y^2=(2x)^2-(9y)^2=(2x-9y)(2x+9y)$$
4. $$0{,}09t^2-121p^2=(0{,}3t)^2-(11p)^2=(0{,}3t-11p)(0{,}3t+11p)$$
5. $$a^2b^2-\frac{16}{9}=(ab)^2-\left(\frac{4}{3}\right)^2=\left(ab-\frac{4}{3}\right)\left(ab+\frac{4}{3}\right)$$
6. $$a^8-x^{10}=(a^4)^2-(x^5)^2=(a^4-x^5)(a^4+x^5)$$
7. $$0{,}04b^4-a^{12}=(0{,}2b^2)^2-(a^6)^2=(0{,}2b^2-a^6)(0{,}2b^2+a^6)$$
8. $$1{,}69y^{14}-900z^8=(1{,}3y^7)^2-(30z^4)^2=(1{,}3y^7-30z^4)(1{,}3y^7+30z^4)$$
9. $$-1+36a^6b^4=36a^6b^4-1=(6a^3b^2)^2-1^2=(6a^3b^2-1)(6a^3b^2+1)$$
10. $$1\frac{24}{25}m^6n^4-1\frac{9}{16}a^2b^8=\frac{49}{25}m^6n^4-\frac{25}{16}a^2b^8$$
    $$=\left(\frac{7}{5}m^3n^2\right)^2-\left(\frac{5}{4}ab^4\right)^2$$
    $$=\left(\frac{7}{5}m^3n^2-\frac{5}{4}ab^4\right)\left(\frac{7}{5}m^3n^2+\frac{5}{4}ab^4\right)$$

Ответ

1) $$(x-5)(x+5)$$;
2) $$(6-4y)(6+4y)$$;
3) $$(2x-9y)(2x+9y)$$;
4) $$(0{,}3t-11p)(0{,}3t+11p)$$;
5) $$\left(ab-\frac{4}{3}\right)\left(ab+\frac{4}{3}\right)$$;
6) $$(a^4-x^5)(a^4+x^5)$$;
7) $$(0{,}2b^2-a^6)(0{,}2b^2+a^6)$$;
8) $$(1{,}3y^7-30z^4)(1{,}3y^7+30z^4)$$;
9) $$(6a^3b^2-1)(6a^3b^2+1)$$;
10) $$\left(\frac{7}{5}m^3n^2-\frac{5}{4}ab^4\right)\left(\frac{7}{5}m^3n^2+\frac{5}{4}ab^4\right)$$