вправа 541 гдз 7 клас алгебра Мерзляк Полонський
7 клас ➠ алгебра ➠ Мерзляк Полонський
Вправа 541
Відповідь:
1) (x - 2)² - 4 =
=(x - 2 - 2)(x - 2 + 2) =
= x(x - 4);
2) (b + 7)² - 100c² =
= (b + 7 - 10c)(b + 7 + 10c);
3) 121 - (b + 7)² =
= (11 - (b + 7))(11 + (b + 7)) =
= (4 - b)(18 + b); \begin{equation}4)a^{4}-\left ( 7b-a^{2} \right )^{2}=\end{equation} \begin{equation}=( a^{2}-( 7b-a^{2} ) ) ( a^{2}+\end{equation} \begin{equation}+( 7b-a^{2} ))=\end{equation} \begin{equation}=7b\left ( 2a^{2}-7b \right );\end{equation} 5) (4x - 9)² - (2x + 19)² =
= ((4x - 9) - (2x + 19))((4x -
- 9) + (2x + 19)) =
= (2x - 28)(6x + 10) =
= 4(x - 14)(3x + 5);
6) (a + b + c)² - (a - b - c)² =
= ((a + b + c) - (a - b - c))((a +
+ b + c) + (a - b - c)) =
= (2b + 2c) · 2a = 4a(b + c).
1) (x - 2)² - 4 =
=(x - 2 - 2)(x - 2 + 2) =
= x(x - 4);
2) (b + 7)² - 100c² =
= (b + 7 - 10c)(b + 7 + 10c);
3) 121 - (b + 7)² =
= (11 - (b + 7))(11 + (b + 7)) =
= (4 - b)(18 + b); \begin{equation}4)a^{4}-\left ( 7b-a^{2} \right )^{2}=\end{equation} \begin{equation}=( a^{2}-( 7b-a^{2} ) ) ( a^{2}+\end{equation} \begin{equation}+( 7b-a^{2} ))=\end{equation} \begin{equation}=7b\left ( 2a^{2}-7b \right );\end{equation} 5) (4x - 9)² - (2x + 19)² =
= ((4x - 9) - (2x + 19))((4x -
- 9) + (2x + 19)) =
= (2x - 28)(6x + 10) =
= 4(x - 14)(3x + 5);
6) (a + b + c)² - (a - b - c)² =
= ((a + b + c) - (a - b - c))((a +
+ b + c) + (a - b - c)) =
= (2b + 2c) · 2a = 4a(b + c).