вправа 484 гдз 7 клас алгебра Мерзляк Полонський

Відповідь:

1) ax² + ay - bx² - by + cx² + cy =
= a(x² + y) - b(x² + y) + c(x² + y) =
= (a - b + c)(x² + y);
2) a²b + a + ab² + b + 3ab + 3 =
= a(ab + 1) + b(ab + 1) + 3(ab + 1) =
= (a + b + 3)(ab + 1);
3) x³ - x² + x²y + x - xy + y =
= x³ + x²y - x² - xy + x + y =
= x²(x + y) - x(x + y) + (x + y) =
= (x² - x + 1)(x + y);
4) m²n + mn - 5 - 5m + n - 5m² =
= m²n - 5m² + mn - 5m + n - 5 =
= m²(n - 5) + m(n - 5) + (n - 5) =
= (m² + m + 1)(n - 5); \begin{equation}5)x^{6}-2x^{5}+4x^{3}-\end{equation} \begin{equation}-8x^{2}+5x-10=\end{equation} \begin{equation}=x^{5}\left ( x-2 \right )+4x^{2}\left ( x-2 \right )+\end{equation} \begin{equation}+5\left ( x-2 \right )=\end{equation} \begin{equation}=\left ( x^{5}+4x^{2}+5 \right )\left ( x-2 \right );\end{equation} \begin{equation}6)a^{3}b+ab^{2}-abc^{3}-\end{equation} \begin{equation}-a^{2}c-bc+c^{4}=\end{equation} \begin{equation}=a^{3}b-a^{2}c+c^{4}-\end{equation} \begin{equation}-abc^{3}+ab^{2}-bc=\end{equation} \begin{equation}=a^{2}\left ( ab-c \right )-c^{3}\left ( ab-c \right )+\end{equation} \begin{equation}+b\left ( ab-c \right )=\end{equation} \begin{equation}=\left ( ab-c \right )\left ( a^{2}-c^{3}+b \right ).\end{equation}