вправа 1168 гдз 7 клас алгебра Мерзляк Полонський

Відповідь:

1) xm - xn + ym - yn =
x(m - n) + y(m - n) =
= (x + y)(m - n);
2) 3a - 3b + ac - bc =
= 3(a - b) + c(a - b) =
= (a - b)(3 + c);
3) 9a - ab - 9 + b =
= a(9 - b) - (9 - b) =
= (a - 1)(9 - b); \begin{equation}4)a^{5}+a^{3}+2a^{2}+2=\end{equation} \begin{equation}=a^{3}\left ( a²+1 \right )+2\left ( a²+1 \right )=\end{equation} \begin{equation}=\left ( a^{3}+2 \right )\left ( a^{2}+1 \right );\end{equation} 5) 6ab² - 3b² + 2a²b - ab =
= 3b²(2a - 1) + ab(2a - 1) =
= (3b² + ab)(2a - 1) =
= b(3b + a)(2a - 1);
6) 2c³ - 5c²d - 4c + 10d =
c²(2c - 5d) - 2(2c - 5d) =
= (c² - 2)(2c - 5d);
7) x³y² - x + x²y³ - y =
= x²y²(x + y) - (x + y) =
= (x²y² - 1)(x + y) =
= (xy - 1)(xy + 1)(x + y);
8) ax² - ay - cy + bx² + cx² - by =
= a(x² - y) + b(x² - y) + c(x² - y) =
= (a + b + c)(x² - y).