Упр.16.5 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) 16-b^2; 5) 4x^2-25; 9) 4a^2 c^2-9x^2 y^2;
2) c^2-49; 6) 81c^2-64d^2; 10) x^24-y^22;
3) (0,04-a^2 ); 7) 0,09x^2-0,25y^2; 11)-1600+a^12;
4) x^2-4/9; 8) a^2 b^4-c^6 d^8; 12) a^18-49/64.

Используем формулу разности квадратов:

$$A^2-B^2=(A-B)(A+B).$$

1. $$16-b^2=4^2-b^2=(4-b)(4+b);$$
2. $$c^2-49=c^2-7^2=(c-7)(c+7);$$
3. $$0,04-a^2=0,2^2-a^2=(0,2-a)(0,2+a);$$
4. $$x^2-\frac{4}{9}=x^2-\left(\frac{2}{3}\right)^2=\left(x-\frac{2}{3}\right)\left(x+\frac{2}{3}\right);$$
5. $$4x^2-25=(2x)^2-5^2=(2x-5)(2x+5);$$
6. $$81c^2-64d^2=(9c)^2-(8d)^2=(9c-8d)(9c+8d);$$
7. $$0,09x^2-0,25y^2=(0,3x)^2-(0,5y)^2=(0,3x-0,5y)(0,3x+0,5y);$$
8. $$a^2b^4-c^6d^8=(ab^2)^2-(c^3d^4)^2=(ab^2-c^3d^4)(ab^2+c^3d^4);$$
9. $$4a^2c^2-9x^2y^2=(2ac)^2-(3xy)^2=(2ac-3xy)(2ac+3xy);$$
10. $$x^{24}-y^{22}=(x^{12})^2-(y^{11})^2=(x^{12}-y^{11})(x^{12}+y^{11});$$
11. $$-1600+a^{12}=a^{12}-1600=(a^6)^2-40^2=(a^6-40)(a^6+40);$$
12. $$a^{18}-\frac{49}{64}=(a^9)^2-\left(\frac{7}{8}\right)^2=\left(a^9-\frac{7}{8}\right)\left(a^9+\frac{7}{8}\right).$$

Ответ

1) $$(4-b)(4+b);$$
2) $$(c-7)(c+7);$$
3) $$(0,2-a)(0,2+a);$$
4) $$\left(x-\frac{2}{3}\right)\left(x+\frac{2}{3}\right);$$
5) $$(2x-5)(2x+5);$$
6) $$(9c-8d)(9c+8d);$$
7) $$(0,3x-0,5y)(0,3x+0,5y);$$
8) $$(ab^2-c^3d^4)(ab^2+c^3d^4);$$
9) $$(2ac-3xy)(2ac+3xy);$$
10) $$(x^{12}-y^{11})(x^{12}+y^{11});$$
11) $$(a^6-40)(a^6+40);$$
12) $$\left(a^9-\frac{7}{8}\right)\left(a^9+\frac{7}{8}\right).$$