вправа 720 гдз 7 клас алгебра Мерзляк Полонський

Відповідь:

1) (m² - 2m)² - 1 =
= (m² - 2m - 1)(m² - 2m + 1) =
= (m² - 2m - 1)(m - 1)²;
2) 16 - (m² + 4m)² =
= (4 - (m² + 4m))(4 + (m² + 4m)) =
= (4 - m² - 4m)(m + 2)²;
3) x² - 18xy + 81y² - z² =
= (x - 9y)² - z² =
= (x - 9y - z)(x - 9y + z);
4) 64x² + 48xy + 9y² - 144 =
= (8x + 3y)² - 12² =
= (8x + 3y - 12)(8x + 3y + 12);
5) c² - a² + 22a - 121 =
= c² - (a² - 22a + 121) =
= c² - (a - 11)² =
= (c - (a - 11))(c + (a - 11)) =
= (c - a + 11)(c + a - 11); \begin{equation}6)100-25y^{2}-60x^{2}y-36x^{4}=\end{equation} \begin{equation}=10^{2}-\left ( 25y^{2}+60x^{2}y+36x^{4} \right )=\end{equation} \begin{equation}=10^{2}-\left ( 5y+6x^{2} \right )=\end{equation} \begin{equation}=\left ( 10-\left ( 5y+6x^{2} \right ) \right )\end{equation} \begin{equation}\left ( 10+\left ( 5y+6x^{2} \right ) \right )=\end{equation} \begin{equation}=\left ( 10-5y-6x^{2} \right )\end{equation} \begin{equation}\left ( 10+5y+6x^{2} \right ).\end{equation}