вправа 685 гдз 7 клас алгебра Мерзляк Полонський

Відповідь:

1) (x + 1)(x² - x + 1) +
+ (2 - x)(4 + 2x + x²) =
= x³ + 1 + 8 - x³ = 9;
2) (x - 4)(x² + 4x +
+ 16) - x(x - 5)(x + 5) =
= x³ - 64 - x(x² - 25) =
= x³ - 64 - x³ + 25x =
= 25x - 64;
3) a(a - 3)² - (a + 3)(a² - 3a + 9) =
= a(a² - 6a + 9) - (a³ + 27) =
= a³ - 6a² + 9a - a³ - 27 =
= -6a² + 9a - 27; \begin{equation}4)\left ( a-1 \right )\left ( a+1 \right )\left ( a^{2}-a+1 \right )\end{equation} \begin{equation}\left ( a^{2}+a+1 \right )\left ( a^{6}+1 \right )\left ( a^{12}+1 \right )=\end{equation} \begin{equation}=\left ( a^{3}-1 \right )\left ( a^{3}+1 \right )\end{equation} \begin{equation}\left ( a^{6}+1 \right )\left ( a^{12}+1 \right )=\end{equation} \begin{equation}=\left ( a^{6}-1 \right )\left ( a^{6}+1 \right )\left ( a^{12}+1 \right )=\end{equation} \begin{equation}=\left ( a^{12}-1 \right )\left ( a^{12}+1 \right )=\end{equation} \begin{equation}=a^{24}-1.\end{equation}