вправа 412 гдз 7 клас алгебра Мерзляк Полонський

Відповідь:

1) x² - 8x + 7 = x² - x - 7x + 7 =
= x(x - 1) - 7(x - 1) =
= (x - 1)(x - 7); \begin{equation}2)y^{2}\left ( y-7 \right )\left ( y+2 \right )=\end{equation} \begin{equation}=y^{2}\left ( y^{2}-5y-14 \right )=\end{equation} \begin{equation}=y^{4}-5y^{3}-14y^{2};\end{equation} 3) (a - 2)(a² + 2a + 4) =
= a³ + 2a² + 4a - 2a² - 4a - 8 =
= a³ - 8; \begin{equation}4)\left ( a-1 \right )\left ( a+1 \right )\left ( a^{2}+1 \right )=\end{equation} \begin{equation}=\left ( a^{2}-1 \right )\left ( a^{2}+1 \right )=\end{equation} \begin{equation}=\left ( a^{2} \right )^{2}-1^{2}=a^{4}-1; \end{equation} \begin{equation}5)\left ( a^{4}-a^{2}+1 \right )\left ( a^{4}+a^{2}+1 \right )=\end{equation} \begin{equation}=\left ( \left ( a^{4}+1 \right )-a^{2} \right )\left ( \left ( a^{4}+1 \right )+a^{2} \right )=\end{equation} \begin{equation}=\left ( a^{4}+1 \right )^{2}-\left ( a^{2} \right )^{2}=\end{equation} \begin{equation}=a^{8}+2a^{4}+1-a^{4}=\end{equation} \begin{equation}=a^{8}+a^{4}+1.\end{equation}