вправа 478 гдз 7 клас алгебра Мерзляк Полонський

Відповідь:

1) a³ + a² + a + 1 =
= a²(a + 1) + (a + 1) =
= (a + 1)(a² + 1); \begin{equation}2)x^{5}-3x^{3}+4x^{2}-12=\end{equation} \begin{equation}=x^{3}\left ( x^{2}-3 \right )+4\left ( x^{2}-3 \right )=\end{equation} \begin{equation}=\left ( x^{3}+4 \right )\left ( x^{2} -3\right );\end{equation} \begin{equation}3)c^{6}-10c^{4}-5c^{2}+50=\end{equation} \begin{equation}=c^{4}\left ( c^{2}-10 \right )-5\left ( c^{2}-10 \right )=\end{equation} \begin{equation}=\left ( c^{4}-5 \right )\left ( c^{2} -10\right );\end{equation} 4) y³ - 18 + 6y² - 3y =
= y³ + 6y² - 3y - 18 =
= y²(y + 6) - 3(y + 6) =
= (y² - 3)(y + 6);
5) a² - ab + ac - bc =
= a(a - b) + c(a - b) = (a + c)(a - b);
6) 20a³bc - 28ac² + 15a²b² - 21bc =
= 4ac(5a²b - 7c) + 3b(5a²b - 7c) =
=(4ac + 3b)(5a²b - 7c);
7) x²y² + xy + axy + a =
= xy(xy + 1) + a(xy + 1) =
= (xy + a)(xy + 1); \begin{equation}8)24x^{6}-44x^{4}y-\end{equation} \begin{equation}-18x^{2}y^{3}+33y^{4}=\end{equation} \begin{equation}=4x^{4}\left ( 6x^{2}-11y \right )-\end{equation} \begin{equation}-3y^{3}\left ( 6x^{2}-11y \right )=\end{equation} \begin{equation}=\left ( 4x^{4}-3y^{3} \right )\left ( 6x^{2}-11y \right ).\end{equation}