Упр.6 Вариант 3 Дидактические материалы ГДЗ Мерзляк Полонский 8 класс (Алгебра)

1) x^2-100; 5) x^4 y^4-9/16;
2) 49-81b^2; 6) m^8-n^10;
3) 9x^2-64y^2; 7) 0,16p^4-q^6;
4) 0,25a^2-1,44b^2; 8)-4+x^4 y^18.

1. $$x^2-100=x^2-10^2=(x-10)(x+10)$$
2. $$49-81b^2=7^2-(9b)^2=(7-9b)(7+9b)$$
3. $$9x^2-64y^2=(3x)^2-(8y)^2=(3x-8y)(3x+8y)$$
4. $$0{,}25a^2-1{,}44b^2=(0{,}5a)^2-(1{,}2b)^2=(0{,}5a-1{,}2b)(0{,}5a+1{,}2b)$$
5. $$x^4y^4-\frac{9}{16}=(x^2y^2)^2-\left(\frac{3}{4}\right)^2=\left(x^2y^2-\frac{3}{4}\right)\left(x^2y^2+\frac{3}{4}\right)$$
6. $$m^8-n^{10}=(m^4)^2-(n^5)^2=(m^4-n^5)(m^4+n^5)$$
7. $$0{,}16p^4-q^6=(0{,}4p^2)^2-(q^3)^2=(0{,}4p^2-q^3)(0{,}4p^2+q^3)$$
8. $$x^4y^{18}-4=(x^2y^9)^2-2^2=(x^2y^9-2)(x^2y^9+2)$$

Ответ

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