вправа 722 гдз 7 клас алгебра Мерзляк Полонський

Відповідь:

1) m² - n² - m + n =
= (m - n)(m + n) - (m - n) =
= (m - n)(m + n - 1);
2) c + d - c² + d² =
= (c + d) - (c + d)(c - d) =
= (c + d)(1 - (c - d)) =
= (c + d)(1 - c + d);
3) 16x² - 25y² - 4x - 5y =
= (4x - 5y)(4x + 5y) - (4x + 5y) =
= (4x + 5y)(4x - 5y - 1);
4) 12a²b³ + 3a³b² + 16b² - a² =
= 3a²b²(4b + a) + (4b + a)(4b - a) =
= (4b + a)(3a²b² + 4b - a);
5) 49c² - 14c + 1 - 21ac + 3a =
= (7c - 1)² - 3a(7c - 1) =
= (7c - 1)(7c - 1 - 3a); \begin{equation}6)ax^{2}+ay^{2}+x^{4}+2x^{2}y^{2}+y^{4}=\end{equation} \begin{equation}=a\left ( x^{2}+y^{2} \right )+\left ( x^{2}+y^{2} \right )^{2}=\end{equation} \begin{equation}=\left ( x^{2}+y^{2} \right )\left ( a+x^{2}+y^{2} \right );\end{equation} 7) 27c³ - d³ + 9c² + 3cd + d² =
= (3c - d)(9c² + 3cd + d²) +
+ (9c² + 3cd + d²) =
= (9c² + 3cd + d²)(3c - d + 1);
8) b³ - 2b² - 2b + 1 =
= (b³ + 1) - (2b² + 2b) =
= (b + 1)(b² - b + 1) - 2b(b + 1) =
= (b + 1)(b² - b + 1 - 2b) =
= (b + 1)(b² - 3b + 1).