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

Разложите на множители:

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

Используем формулу разности квадратов: $$a^2-b^2=(a-b)(a+b).$$

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