вправа 718 гдз 7 клас алгебра Мерзляк Полонський

Відповідь:

1) 15cx + 2cy - cxy - 30c =
= 15c(x - 2) - cy(x - 2) =
= (15c - cy)(x - 2) =
= c(15 - y)(x - 2);
2) 35a² - 42ab + 10a²b - 12ab² =
= 5a²(7 + 2b) - 6ab(7 + 2b) =
= (5a² - 6ab)(7 + 2b) =
= a(5a - 6b)(7 + 2b);
3) x³ + x²y + x² + xy =
= x²(x + y) + x(x + y) =
= (x² + x)(x + y) =
= x(x + 1)(x + y); \begin{equation}4)mn^{4}-n^{4}+mn^{3}-n^{3}=\end{equation} \begin{equation}=n^{4}\left ( m-1 \right )+n^{3}\left ( m-1 \right )=\end{equation} \begin{equation}=\left ( n^{4}+n^{3} \right )\left ( m-1 \right )=\end{equation} \begin{equation}=n^{3}\left ( n+1 \right )\left ( m-1 \right ).\end{equation}