Упр.13.19 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) (2x-6)^2; 2) (5y+5)^2;
3) (36x+30y)^2; 4) (2x+4)^4;
5) (6x-9y)^3; 6) (a^2+ab)^2;
7) (-7a-14ab)^2; 8) (3c^4-6c^3 )^4.

1. $$\left(2x-6\right)^2=\left(2(x-3)\right)^2=2^2(x-3)^2=4(x-3)^2$$
2. $$\left(5y+5\right)^2=\left(5(y+1)\right)^2=5^2(y+1)^2=25(y+1)^2$$
3. $$\left(36x+30y\right)^2=\left(6(6x+5y)\right)^2=6^2(6x+5y)^2=36(6x+5y)^2$$
4. $$\left(2x+4\right)^4=\left(2(x+2)\right)^4=2^4(x+2)^4=16(x+2)^4$$
5. $$\left(6x-9y\right)^3=\left(3(2x-3y)\right)^3=3^3(2x-3y)^3=27(2x-3y)^3$$
6. $$\left(a^2+ab\right)^2=\left(a(a+b)\right)^2=a^2(a+b)^2$$
7. $$\left(-7a-14ab\right)^2=\left(-7a(1+2b)\right)^2=(-7a)^2(1+2b)^2=49a^2(1+2b)^2$$
8. $$\left(3c^4-6c^3\right)^4=\left(3c^3(c-2)\right)^4=(3c^3)^4(c-2)^4=81c^{12}(c-2)^4$$

Ответ

1) $$4(x-3)^2$$; 2) $$25(y+1)^2$$; 3) $$36(6x+5y)^2$$; 4) $$16(x+2)^4$$; 5) $$27(2x-3y)^3$$; 6) $$a^2(a+b)^2$$; 7) $$49a^2(1+2b)^2$$; 8) $$81c^{12}(c-2)^4$$.