вправа 1133 гдз 7 клас алгебра Мерзляк Полонський
7 клас ➠ алгебра ➠ Мерзляк Полонський
Вправа 1133
Відповідь:
1) 4kn + 6ak + 6an + 9a² =
= 2n(2k + 3a) + 3a(2k + 3a) =
= (2n + 3a)(2k + 3a); \begin{equation}2)b^{6}-4b^{4}+12b^{2}-9=\end{equation} \begin{equation}=b^{6}-\left ( 4b^{4}-12b^{2}+9 \right )=\end{equation} \begin{equation}=b^{6}-\left ( 2b^{2}-3 \right )^{2}=\end{equation} \begin{equation}=\left ( b^{3}-2b^{2}+3 \right )\left ( b^{3}+2b^{2}-3 \right );\end{equation} \begin{equation}3)y^{4}\left ( x^{2}+8x+16 \right )-a^{8}=\end{equation} \begin{equation}=\left ( y^{2}\left ( x+4 \right ) \right )^{2}-a^{8}=\end{equation} \begin{equation}=\left ( y^{2}\left ( x+4 \right )-a^{4} \right )\end{equation} \begin{equation}\left ( y^{2}\left ( x+4 \right )+a^{4} \right )=\end{equation} \begin{equation}=\left ( y^{2}x+4y^{2}-a^{4} \right )\end{equation} \begin{equation}\left ( y^{2}x+4y^{2}+a^{4} \right );\end{equation} 4) 9x² - 6x - 35 = (3x - 1)² - 36 =
= (3x - 1 - 6)(3x - 1 + 6) =
= (3x - 7)(3x + 5).
1) 4kn + 6ak + 6an + 9a² =
= 2n(2k + 3a) + 3a(2k + 3a) =
= (2n + 3a)(2k + 3a); \begin{equation}2)b^{6}-4b^{4}+12b^{2}-9=\end{equation} \begin{equation}=b^{6}-\left ( 4b^{4}-12b^{2}+9 \right )=\end{equation} \begin{equation}=b^{6}-\left ( 2b^{2}-3 \right )^{2}=\end{equation} \begin{equation}=\left ( b^{3}-2b^{2}+3 \right )\left ( b^{3}+2b^{2}-3 \right );\end{equation} \begin{equation}3)y^{4}\left ( x^{2}+8x+16 \right )-a^{8}=\end{equation} \begin{equation}=\left ( y^{2}\left ( x+4 \right ) \right )^{2}-a^{8}=\end{equation} \begin{equation}=\left ( y^{2}\left ( x+4 \right )-a^{4} \right )\end{equation} \begin{equation}\left ( y^{2}\left ( x+4 \right )+a^{4} \right )=\end{equation} \begin{equation}=\left ( y^{2}x+4y^{2}-a^{4} \right )\end{equation} \begin{equation}\left ( y^{2}x+4y^{2}+a^{4} \right );\end{equation} 4) 9x² - 6x - 35 = (3x - 1)² - 36 =
= (3x - 1 - 6)(3x - 1 + 6) =
= (3x - 7)(3x + 5).